I mean... call of duty is a hell of a lot of games, so no idea which one you play. Most of them are pretty old so modern hardware should easily handle it. I don't care for FPS so no idea what the actual situation is there. I do know that proton seems to perform very well for me in other games on the linux living room gaming system and the steam deck (Xorg for both). Valve claims in general outperforms windows for similar hardware. But I suppose it could depend on your graphics card and drivers.