This is just my experience, but I have had next to zero issues running games on the Deck that were related to the platform. Most problems I’ve encountered are along the lines of the game being KBM-centric and it being difficult to play with the controller inputs.
The only Linux-specific issues I can’t think of are related to trying to install or mod games outside of Steam (Skyrim in particular is far more difficult to mod on Linux than I expected).
All fair. I haven’t tried either with the Deck, though that’s more because I don’t want to try games from either platform with a controller. I have had success running both on my Linux desktop, though.