First of all, to see a complete list of configure options refer to ./configure --help.
According to the FFmpeg documentation...
This isn't actually the documentation but is a wiki that is editable by anyone, so like any wiki you may want to independently verify any claims.
This made me wonder what other such options FFmpeg can be compiled with in order to give me the best build for creating the most efficient (i.e. the highest quality at the lowest bitrate) audio.
This is currently Opus audio. Enable it with --enable-libopus, and use the latest version of libopus if you want to take advantage of recent development activity.
There are claims that the Sox audio resampler is better than the built-in resampler in FFmpeg. I haven't tried it much myself. Enable it with --enable-libsoxr.
What advantages does compiling with
--enable-nonfreeoffer?
This option alone gives no advantages. It is required for some external libraries that are considered to be non-free. You can view which libraries require this in the source code of the configure file: refer to EXTERNAL_LIBRARY_NONFREE_LIST (and HWACCEL_LIBRARY_NONFREE_LIST). As of this answer these include: decklink, libndi_newtek, libfdk_aac, openssl, libtls (and cuda_nvcc, cuda_sdk, libnpp).
A disadvantage of using --enable-nonfree is that the resulting build will be non-free and therefore non-redistributable.
What advantages does not compiling with
--enable-gploffer?
Slightly faster to compile. Somewhat smaller resulting executable file size. LGPL 2.1 license instead of GPL 2. However, these may not be of any concern to you.
See LICENSE.md included in the source code for a complete list of what requires --enable-gpl.
First of all, to see a complete list of configure options refer to ./configure --help.
According to the FFmpeg documentation...
This isn't actually the documentation but is a wiki that is editable by anyone, so like any wiki you may want to independently verify any claims.
This made me wonder what other such options FFmpeg can be compiled with in order to give me the best build for creating the most efficient (i.e. the highest quality at the lowest bitrate) audio.
This is currently Opus audio. Enable it with --enable-libopus, and use the latest version of libopus if you want to take advantage of recent development activity.
There are claims that the Sox audio resampler is better than the built-in resampler in FFmpeg. I haven't tried it much myself. Enable it with --enable-libsoxr.
What advantages does compiling with
--enable-nonfreeoffer?
This option alone gives no advantages. It is required for some external libraries that are considered to be non-free. You can view which libraries require this in the source code of the configure file: refer to EXTERNAL_LIBRARY_NONFREE_LIST (and HWACCEL_LIBRARY_NONFREE_LIST). As of this answer these include: decklink, libndi_newtek, libfdk_aac, openssl, libtls (and cuda_nvcc, cuda_sdk, libnpp).
A disadvantage of using --enable-nonfree is that the resulting build will be non-free and therefore non-redistributable.
What advantages does not compiling with
--enable-gploffer?
Slightly faster to compile. Somewhat smaller resulting executable file size. LGPL 2.1 license instead of GPL 2. However, these may not be of any concern to you.
See LICENSE.md included in the source code for a complete list of what requires --enable-gpl.
Thanks to llogan for pointing out that the full list of configuration options can be found by doing ./configure --help in the directory containing the FFmpeg sources. Unfortunately this information isn't documented anywhere else, so to make it available without requiring that FFmpeg's sources are downloaded, I've reproduced them below.
Note that I've only reproduced the configuration options that enable/disable support for a particular external library or hardware acceleration feature - general program configuration or debugging options have been omitted. Each option is followed by a description in square brackets of whether the option is enabled by default in FFmpeg or whether support for it is autodetected:
Licensing options:
--enable-gpl allow use of GPL code, the resulting libs and binaries will be under GPL [no]
--enable-version3 upgrade (L)GPL to version 3 [no]
--enable-nonfree allow use of nonfree code, the resulting libs and binaries will be unredistributable [no]
External library support:
Using any of the following switches will allow FFmpeg to link to the
corresponding external library. All the components depending on that library
will become enabled, if all their other dependencies are met and they are not
explicitly disabled. E.g. --enable-libwavpack will enable linking to
libwavpack and allow the libwavpack encoder to be built, unless it is
specifically disabled with --disable-encoder=libwavpack.
Note that only the system libraries are auto-detected. All the other external
libraries must be explicitly enabled.
Also note that the following help text describes the purpose of the libraries
themselves, not all their features will necessarily be usable by FFmpeg.
--disable-alsa disable ALSA support [autodetect]
--disable-appkit disable Apple AppKit framework [autodetect]
--disable-avfoundation disable Apple AVFoundation framework [autodetect]
--enable-avisynth enable reading of AviSynth script files [no]
--disable-bzlib disable bzlib [autodetect]
--disable-coreimage disable Apple CoreImage framework [autodetect]
--enable-chromaprint enable audio fingerprinting with chromaprint [no]
--enable-frei0r enable frei0r video filtering [no]
--enable-gcrypt enable gcrypt, needed for rtmp(t)e support if openssl, librtmp or gmp is not used [no]
--enable-gmp enable gmp, needed for rtmp(t)e support if openssl or librtmp is not used [no]
--enable-gnutls enable gnutls, needed for https support if openssl, libtls or mbedtls is not used [no]
--disable-iconv disable iconv [autodetect]
--enable-jni enable JNI support [no]
--enable-ladspa enable LADSPA audio filtering [no]
--enable-libaom enable AV1 video encoding/decoding via libaom [no]
--enable-libaribb24 enable ARIB text and caption decoding via libaribb24 [no]
--enable-libass enable libass subtitles rendering, needed for subtitles and ass filter [no]
--enable-libbluray enable BluRay reading using libbluray [no]
--enable-libbs2b enable bs2b DSP library [no]
--enable-libcaca enable textual display using libcaca [no]
--enable-libcelt enable CELT decoding via libcelt [no]
--enable-libcdio enable audio CD grabbing with libcdio [no]
--enable-libcodec2 enable codec2 en/decoding using libcodec2 [no]
--enable-libdav1d enable AV1 decoding via libdav1d [no]
--enable-libdavs2 enable AVS2 decoding via libdavs2 [no]
--enable-libdc1394 enable IIDC-1394 grabbing using libdc1394 and libraw1394 [no]
--enable-libfdk-aac enable AAC de/encoding via libfdk-aac [no]
--enable-libflite enable flite (voice synthesis) support via libflite [no]
--enable-libfontconfig enable libfontconfig, useful for drawtext filter [no]
--enable-libfreetype enable libfreetype, needed for drawtext filter [no]
--enable-libfribidi enable libfribidi, improves drawtext filter [no]
--enable-libgme enable Game Music Emu via libgme [no]
--enable-libgsm enable GSM de/encoding via libgsm [no]
--enable-libiec61883 enable iec61883 via libiec61883 [no]
--enable-libilbc enable iLBC de/encoding via libilbc [no]
--enable-libjack enable JACK audio sound server [no]
--enable-libklvanc enable Kernel Labs VANC processing [no]
--enable-libkvazaar enable HEVC encoding via libkvazaar [no]
--enable-liblensfun enable lensfun lens correction [no]
--enable-libmodplug enable ModPlug via libmodplug [no]
--enable-libmp3lame enable MP3 encoding via libmp3lame [no]
--enable-libopencore-amrnb enable AMR-NB de/encoding via libopencore-amrnb [no]
--enable-libopencore-amrwb enable AMR-WB decoding via libopencore-amrwb [no]
--enable-libopencv enable video filtering via libopencv [no]
--enable-libopenh264 enable H.264 encoding via OpenH264 [no]
--enable-libopenjpeg enable JPEG 2000 de/encoding via OpenJPEG [no]
--enable-libopenmpt enable decoding tracked files via libopenmpt [no]
--enable-libopus enable Opus de/encoding via libopus [no]
--enable-libpulse enable Pulseaudio input via libpulse [no]
--enable-librsvg enable SVG rasterization via librsvg [no]
--enable-librubberband enable rubberband needed for rubberband filter [no]
--enable-librtmp enable RTMP[E] support via librtmp [no]
--enable-libshine enable fixed-point MP3 encoding via libshine [no]
--enable-libsmbclient enable Samba protocol via libsmbclient [no]
--enable-libsnappy enable Snappy compression, needed for hap encoding [no]
--enable-libsoxr enable Include libsoxr resampling [no]
--enable-libspeex enable Speex de/encoding via libspeex [no]
--enable-libsrt enable Haivision SRT protocol via libsrt [no]
--enable-libssh enable SFTP protocol via libssh [no]
--enable-libtensorflow enable TensorFlow as a DNN module backend for DNN based filters like sr [no]
--enable-libtesseract enable Tesseract, needed for ocr filter [no]
--enable-libtheora enable Theora encoding via libtheora [no]
--enable-libtls enable LibreSSL (via libtls), needed for https support if openssl, gnutls or mbedtls is not used [no]
--enable-libtwolame enable MP2 encoding via libtwolame [no]
--enable-libv4l2 enable libv4l2/v4l-utils [no]
--enable-libvidstab enable video stabilization using vid.stab [no]
--enable-libvmaf enable vmaf filter via libvmaf [no]
--enable-libvo-amrwbenc enable AMR-WB encoding via libvo-amrwbenc [no]
--enable-libvorbis enable Vorbis en/decoding via libvorbis, native implementation exists [no]
--enable-libvpx enable VP8 and VP9 de/encoding via libvpx [no]
--enable-libwavpack enable wavpack encoding via libwavpack [no]
--enable-libwebp enable WebP encoding via libwebp [no]
--enable-libx264 enable H.264 encoding via x264 [no]
--enable-libx265 enable HEVC encoding via x265 [no]
--enable-libxavs enable AVS encoding via xavs [no]
--enable-libxavs2 enable AVS2 encoding via xavs2 [no]
--enable-libxcb enable X11 grabbing using XCB [autodetect]
--enable-libxcb-shm enable X11 grabbing shm communication [autodetect]
--enable-libxcb-xfixes enable X11 grabbing mouse rendering [autodetect]
--enable-libxcb-shape enable X11 grabbing shape rendering [autodetect]
--enable-libxvid enable Xvid encoding via xvidcore, native MPEG-4/Xvid encoder exists [no]
--enable-libxml2 enable XML parsing using the C library libxml2, needed for dash demuxing support [no]
--enable-libzimg enable z.lib, needed for zscale filter [no]
--enable-libzmq enable message passing via libzmq [no]
--enable-libzvbi enable teletext support via libzvbi [no]
--enable-lv2 enable LV2 audio filtering [no]
--disable-lzma disable lzma [autodetect]
--enable-decklink enable Blackmagic DeckLink I/O support [no]
--enable-mbedtls enable mbedTLS, needed for https support if openssl, gnutls or libtls is not used [no]
--enable-mediacodec enable Android MediaCodec support [no]
--enable-libmysofa enable libmysofa, needed for sofalizer filter [no]
--enable-openal enable OpenAL 1.1 capture support [no]
--enable-opencl enable OpenCL processing [no]
--enable-opengl enable OpenGL rendering [no]
--enable-openssl enable openssl, needed for https support if gnutls, libtls or mbedtls is not used [no]
--disable-sndio disable sndio support [autodetect]
--disable-schannel disable SChannel SSP, needed for TLS support on Windows if openssl and gnutls are not used [autodetect]
--disable-sdl2 disable sdl2 [autodetect]
--disable-securetransport disable Secure Transport, needed for TLS support on OSX if openssl and gnutls are not used [autodetect]
--enable-vapoursynth enable VapourSynth demuxer [no]
--disable-xlib disable xlib [autodetect]
--disable-zlib disable zlib [autodetect]
The following libraries provide various hardware acceleration features:
--disable-amf disable AMF video encoding code [autodetect]
--disable-audiotoolbox disable Apple AudioToolbox code [autodetect]
--enable-cuda-nvcc enable Nvidia CUDA compiler [no]
--disable-cuvid disable Nvidia CUVID support [autodetect]
--disable-d3d11va disable Microsoft Direct3D 11 video acceleration code [autodetect]
--disable-dxva2 disable Microsoft DirectX 9 video acceleration code [autodetect]
--disable-ffnvcodec disable dynamically linked Nvidia code [autodetect]
--enable-libdrm enable DRM code (Linux) [no]
--enable-libmfx enable Intel MediaSDK (AKA Quick Sync Video) code via libmfx [no]
--enable-libnpp enable Nvidia Performance Primitives-based code [no]
--enable-mmal enable Broadcom Multi-Media Abstraction Layer (Raspberry Pi) via MMAL [no]
--disable-nvdec disable Nvidia video decoding acceleration (via hwaccel) [autodetect]
--disable-nvenc disable Nvidia video encoding code [autodetect]
--enable-omx enable OpenMAX IL code [no]
--enable-omx-rpi enable OpenMAX IL code for Raspberry Pi [no]
--enable-rkmpp enable Rockchip Media Process Platform code [no]
--disable-v4l2-m2m disable V4L2 mem2mem code [autodetect]
--disable-vaapi disable Video Acceleration API (mainly Unix/Intel) code [autodetect]
--disable-vdpau disable Nvidia Video Decode and Presentation API for Unix code [autodetect]
--disable-videotoolbox disable VideoToolbox code [autodetect]
Also note that some codecs above, such as Xvid and Vorbis, already have encoders native to FFmpeg and don't require that any additional encoders be enabled.
Additional information on licensing options can be found from this screenshot of the Media Auto Build Suite, which I found to contain the best explanation I've come across so far of what the licensing options mean and what their implications are:

Hello, I am relatively new to FFmpeg.
I have been working on a customized version of FFmpeg in order to resolve the issue where the HEVC_CUVID decoder fails to retrieve HDR10+ side data after decoding.
To achieve this, I had to modify certain C files and compile them accordingly.
However, I encountered performance concerns with my current build; while Gyan's library achieves approximately 34 FPS, my custom build falls short at less than 9 FPS.
Moreover, it seems that Nvidia hardware acceleration features such as CUVID, FFNVCODEC, and NVDEC are not available or enabled in my build.
My configuration options include:
./configure --toolchain=msvc --arch=x86_64 --enable-yasm --disable-x86asm --enable-asm --enable-shared --enable-w32threads --disable-programs --disable-doc --disable-static --prefix=/c/ffmpeg3.3/DLLS
I would greatly appreciate any guidance on resolving these two issues simultaneously.
Thank you for your time and assistance.
install prefix /c/ffmpeg3.3/DLLS source path . C compiler cl.exe C library msvcrt ARCH x86 (generic) big-endian no runtime cpu detection yes standalone assembly no x86 assembler nasm MMX enabled yes MMXEXT enabled yes 3DNow! enabled yes 3DNow! extended enabled yes SSE enabled yes SSSE3 enabled yes AESNI enabled yes AVX enabled yes AVX2 enabled yes AVX-512 enabled yes AVX-512ICL enabled yes XOP enabled yes FMA3 enabled yes FMA4 enabled yes i686 features enabled yes CMOV is fast yes EBX available no EBP available no debug symbols yes strip symbols no optimize for size no optimizations yes static no shared yes postprocessing support no network support yes threading support w32threads safe bitstream reader yes texi2html enabled no perl enabled yes pod2man enabled yes makeinfo enabled no makeinfo supports HTML no xmllint enabled no External libraries: mediafoundation schannel External libraries providing hardware acceleration: d3d11va d3d12va dxva2