I'd have to look back at benchmarks, but I think there's a few factors here - price and next upgrade. From what I remember those two were fairly similar in performance and just traded blows between games.
AM5 is still a bit more expensive as a platform, but you can probably get a decent board and possibly upgrade the cpu&gpu in a few years to save longer term if you do a partial upgrade.
The 13600kf build would likely be cheaper, but the 13th gen i think is the last before intel changes the socket. Your next build after this may be more expensive by needing more parts (depending on when you upgrade).
Depending on when you build, you might wanna check for deals on the 7800x3d as it's dropped to like 385$ recently. the uplift in some games is pretty substantial and it's a beast for gaming. If it drops below that, it may be worth using that over the 7700. If price is an absolute limit, you'll definitely save with the 13th gen intel.