Those generic Xbox 360 adapter work fine, they are detected without issue on the PI. On Windows you need to set the driver old school by hand, once you do that you are done.
I have a good collection of controller
Steam Controller= Best for Windows, the way you are allowed to set it up, is PERFECT. On the PI works fine nothing great
Xbox 360= Wireless is great but i don't to have the dongle
PS3= Works fine
PS4= i fell like there is a delay and to be honest not my favourite joystick
Trust generic control = Works like it should but the quality is not the best
Ipega 9025 = Works fine, but it is too small and the analogs are a bit loss
Razer Serval = Works like a charm, perfect felling for the buttons the analogs are amazing, they are pressure sensitive, the DPAD is Ok... i love it for my Android and for the PI.. The biggest DOWNSIDE of the Servel is way too expensive.