Interestingly enough, I've had games that had both a native Linux port and Windows version, and the Windows version through Proton ran better than the native Linux version. This ended up being true for Civ5, Civ6 and Cities Skylines (1).
With those admittedly limited examples though, I don't experience the same ranking in performance, but I attribute that to my non-gaming hardware vs. any problem with Linux or Proton/Wine. I play on a laptop with an Nvidia 3050 laptop GPU, and I get much better performance in Windows still. In Cities Skylines, for example, I'll get ~20 fps on Linux via Proton (but I do experience what you said, it's consistent no major spikes or drops) while on Windows I get between 45-60fps up until about 15k population or so.
Other games, despite working, remain unplayable to me due to performance. I can play Diablo 4 on windows no problem on medium settings, but even on low it's just too unresponsive on Linux.
Anyway, just my anecdotal experience. Those with dedicated gaming rigs will be more than fine with Linux, but those of us on underpowered hardware still seem better off with Windows, unfortunately.