A 13900k is significantly faster than the 12900ks. It has about 10% better single P-core performance, 8 more E-cores, significantly more L2 cache, etc. Overall, barring GPU or memory bottlenecking (which, depending on your other parts, may happen in some games), you can achieve at least 10-15% more FPS in games by going with the 13th gen part. At those prices, the 12900ks is a slightly better value (though neither is exactly a bang for your buck choice) if gaming is your primary workload while extremely heavily threaded workloads would favor the 8 more threads of the 13900k, but overall if you can afford either there's not a "wrong" decision. I'd probably go 13th gen between the two if I could afford it, though especially if you don't completely need 32 threads (which you clearly don't if you're considering 12900KS), the "best" option for your money is clear: neither.

A 13700K has exactly the same core config as 12th gen i9s (8 P, 8 E), and while it technically doesn't get peak boost clocks as high as the 12900KS (5.4GHz vs 5.5GHz is a negligible difference), its single thread performance is slightly higher due to IPC improvements, it has double the L2 cache of the 12900KS due to Raptor Lake's superior cache per core, and overall provides 99% of the gaming performance of the 13900K while still slightly beating the 12900KS in productivity tasks. And as to price comparison? The 12900KS on Canadian PCPartpicker is CAD$665, while the 13700K is CAD$546. So again, unless you need absolutely insane multithreaded performance, the answer is just to get a 13700K.

An alternative if you don't already have an LGA1700 motherboard (which it sounds like you may, but worth considering if you don't) and you don't even need the thread count of the 13700K (you probably don't) might be the Ryzen 7700X- it's about CAD$450 and is within about 3-4% of the gaming performance of the 13700K while having lower peak power draw and still having a very solid 8 cores/16 threads. It still beats the 12900KS in gaming performance by about 8%, but if you already have a Z690 or Z790 then you won't save enough to make it worth buying over an Intel equivalent.