Some emulators will not work with xinput, (either of those).
HID was the standard for many years. and recent emulators used xinput. Some only xinput, its a mess but that's why adapters exist that do both.
Bliss-Box.net is the best for HID (if you have originals), where xbox like are the best for xinput. If you want a HID without using originals, consider the switch pro.
Or look in to apps like x360ce
I like the idea of Bliss-Box because it works on some usb consoles and PC's and with the upcoming Brdige adapter, it can also be xinput and work on other non USB consoles as well.