This blanket statement is not generally applicable. It can depend on rendering tech used, the game, and hardware. And this is going to be an issue in bleeding edge games mostly.
Borderlands 2, for example, plays fine for me on a i7 930, with a GTX 570. An older rig.
Dota 2 with OpenGL rendering hits or exceeds the Windows FPS when run on Linux.
Switch to Vulkan though and it craters.
Source engine games with OpenGL rendering often outperform Windows.
https://en.wikipedia.org/wiki/Nissan_Motors_vs._Nissan_Compu...