I think all USB gamepads work, so long as they're detected as a game pad. XBox controllers are the "default" controller and tend to work correctly right away. If you connect a controller and find the buttons are all mixed up, then you could program a "Choose your input" menu system, where the player can click on, for example, jump, and then press a button on their controller to assign jumping to a button.
I've tested PS4, third-party switch controller, third-party dance mat, and all work fine in Construct.
The only example of something NOT working, would be a non-gamepad item, like a MIDI piano keyboard, as these are detected as MIDI devices rather than USB game pads.