They're [probably] all the same (gold has an extra version -- see the end of this post).
But consider the rest of this answer code-golf for the best way to extract the versions.

dpkg -L binutils | grep "/usr/bin/" | xargs -i sh -c "{} --version"

Does pretty much what roadmr's does.

dpkg -L binutils | xargs -i sh -c "{} --version 2>/dev/null || exit 0"

Tries to run everything dpkg -L ... outputs. Obviously only the executables will run so we just need to redirect error (and make xargs ignore them).

dpkg -L binutils | xargs -i bash -c '[[ -x "{}" && -f "{}" ]] && {} --version'

Test that we're dealing with an executable file rather than filtering path.

sudo apt-get install parallel
dpkg -L binutils | grep /usr/bin/ | parallel {} --version
dpkg -L binutils | parallel {} --version 2>/dev/null
dpkg -L binutils | parallel '[[ -x "{}" && -f "{}" ]] && {} --version'

This time we use GNU parallel to do the same approaches. parallel lets us skip over certain inconveniences in xargs (like it not being able to skip over any non-zero exit code. man parallel is a genuinely good read.

With all that said, while shorter, all my examples fork out into a new shell (unavoidable with xargs, and sort of the point of parallel) so they're all somewhat slower than roadmr's. The first is the quickest.

Edit: Until now...

sh <(dpkg -L binutils | awk '/bin\// {print $0 " --version"}')

Only two forks (sort of) and it's as fast as the for loop (while much shorter).

Edit: They're actually not quite the same. gold has a secondary version (1.11) which the other commands don't.

$ sh <(dpkg -L binutils | awk '/bin\// {print $0 " --version"}') | \
    grep Binutils | sort -u | column -t
GNU  addr2line  (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  ar         (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  assembler  (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  c++filt    (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  dwp        (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  elfedit    (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  gold       (GNU  Binutils  for  Ubuntu   2.23.52.20130913)  1.11
GNU  gprof      (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  ld         (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  nm         (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  objcopy    (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  objdump    (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  ranlib     (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  readelf    (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  size       (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  strings    (GNU  Binutils  for  Ubuntu)  2.23.52.20130913
GNU  strip      (GNU  Binutils  for  Ubuntu)  2.23.52.20130913

Install the following packages via apt-get or Synaptic:

• gcc
• binutils
• make
• linux-source

The last package always contains the sources for the newest kernel. If you are running an older kernel, you should get the sources for that, e.g. linux-source-3.0.0 . If you don't know, which kernel you are running, type uname -a in a terminal.

Yes, with ld -v you can view the version of binutils (in your case is 2.24)