If you have an OLED, I highly recommend a dualsense controller over Xbox since it added bluetooth-to-wake. Dualsense has gyro, rechargeable, and better back button mods in my experience. Plus, if you use the Xbox adapter, you have to reinstall the driver's after every OS Update (although I believe there are some ways to get around this)
This is true! I always had issues with Xbox over Bluetooth though, so I went with the adapter route which worked well. Granted I haven't tried Xbox Bluetooth on steam deck, only a Windows PC. Does it work well?