There's another way to get a PlayStation controller to work on an Xbox. More specifically, it involves using a bit of digital trickery to make the connection work. All you need is a PlayStation ...
If Steam is where you play all of your games ... Lots of games also recognize the PlayStation controller and will show you the correct button icons, or offer the option to manually toggle them ...
You'll find that such games aren't meant to be played with anything other than a mouse and keyboard, and PlayStation controllers don't have enough buttons to handle all their various inputs.