Lately, I've been using my Steam Deck docked with a keyboard and mouse, but I can't find any keyboard shortcuts that work for bringing up the Steam menu and QAM. I've read that Ctrl + 1 and Ctrl + 2 can do this, but apparently doesn't work in-game...
I don't think there's a significant performance difference but I haven't tested it. One difference is that Desktop mode still uses X11 whereas Gaming mode uses Wayland. That can effect some programs but I don't think any games mind which is used.