The only 360 controllers I can use for retro games at all are the ones with the redesigned "transforming" pad. Even then, they are mediocre at best. The standard 360 controllers have issues with the downward directional button in particular turning to mush over time. I've modded so many of these controllers just to keep them working. Of course that doesn't matter much for most actual 360 games. Oddly, the wireless ones seem to wear out much faster than the wires versions. I've never figured out why because the d pad parts on both kinds are completely interchangeable.

It's a real shame as they are compatible with every consumer electronic device created by man. I'm pretty sure you could go to the space history museum, install x-input drivers on an apollo capsule, and go to town.