As Megavolt has said, and can be also seen in the Benchmarks at Phoronix, you won’t necessarily see better performance in every game (and anyway performance-wise nVidias Linux drivers are ok most of the time).
Sad fact (for gamers) is that Linux is still an afterthought to software and hardware devs when it comes to gaming performance. This can be seen e.g. in the much larger variance between individual games and cards with both vendors. One game you’d like to play might run absolutely great, but the next will be having issues.
If your main intent is gaming and you want reliable performance, Windows is still the way to go.
A big reason why AMD’s drivers nowadays have a better reputation than nVidias is also because AMD’s linux drivers now are open source, well implemented into the ecosystem and generally “just work” without much intervention required (there are exceptions in particular for very new hardware, which often take some months to settle).
nVidia’s closed model has drawn some fire recently also on an ideological basis and I think some distros are contemplating dropping them due to some recent shennanigans surrounding attempts to circumvent open source licenses.
Coming back to your problem: it would be best to compare with other people running similar hardware, so you get a better picture of what to expect. I don’t own any of those games, however.
My experience with the ones I do own has been similar to what one sees in the Phoronix benches - some run great, others have issues. On average it’s similar to windows, but there’s no guarantee.
E.g. Serious Sam 3 BFE is having high fps on Linux, similar to Windows, but Windows still feels smoother - apparently there’s an issue with shader caching under Linux.
OpenMW (open source Morrowind engine implementation) OTOH runs much better on Linux than on WIndows for me.
Black Mesa ran stuttery and had glitches, so I quickly switched to Windows for playing it, while other games with the engine (L4D 2, HL: EP2) run perfectly fine.