The UltraStik 360 uses the UBS-A connector. It does not use any of the other connectors, so it does not matter what top jack option you choose.
I think the decision comes down to if you can operate any buttons or switches. If you have enough movement to use an UltraStik, then you are more likely to want to use other input devices, so the input option makes sense.
The output option allows the quadstick to control something just like a switch and is useful for someone with a high-level injury to operate a couple of things using the quadstick's relay outputs.