I tried both, a Microsoft Xbox Series X Wireless Controller, and a DualShock 4. I’m not happy with either, but if I had to choose, I’d go with the DualShock.

The Xbox gamepad does not have a gyro sensor, and also does not have a touchpad. Furthermore, the build quality is really bad. I also have an Xbox 360 gamepad (which doesn’t have Bluetooth, so it can’t be connected to the Deck without an expensive USB receiver), and putting the Xbox 360 and Xbox Series X gamepads side by side shows just how horrible the new gamepads are… Another issue with the Xbox Series X gamepad is that you probably need to update the firmware before you can pair it properly with the Steam Deck, what requires access to a Windows PC or an Xbox console (I couldn’t get the firmware update to work from within a VM, even though the USB forwarding worked). The main advantage of the Xbox Series X gamepad is, that it uses regular AA accumulators, so you don’t need to worry about the battery dying.

The PS4 gamepad on the other hand has a touchpad, a gyro sensor, and the build quality is pretty good. It does have other drawbacks though: Unlike the Xbox gamepad it does not use normal AA batteries, but has a built-in battery that isn’t as straightforward to replace. Also, its Bluetooth tends to severely interfere with the Steam Deck’s WLAN, up to the point that the WLAN connection just dies when using the PS4 gamepad. (I solved that by buying a wired Ethernet adapter and connecting that over USB, but that’s not always an option…)