See the top of Gaming with CachyOS Guide | CachyOS
Some games run better, some (primarily through Proton or using DX12, or if using Nvidia) run worse, most are similar. YouTube comparison videos tend to cherry-pick games that run better on Linux, if you want specific examples.
Also, “on Linux” is a nebulous term, as it depends on distro, kernel tweaks, DE and setup, GPU vendor and drivers, game-specific tweaks (like through Steam launch options), Proton version (or native), etc. etc.