I was pretty sure SOTN didn't support analog controls... luckily my game case was sitting right next to me as I was reading the posts... XD. SOTN *doesn't* support analog controls. Not sure if Megaman X6 does, but it doesn't seem all that logical to me for a Megaman game to bother with analog controls. FFIX does support analog controls... make sure you follow patrickp's advice on the memory card situation.
I thought the 360 controllers needed modified drivers to work properly with certain programs (pSX being one of them). Not sure if it was just a rumble problem, but you should check
this post on the official forums to try out the drivers reported (they were said to fully work with pSX, so if they don't work for you, odds are good that you're missing something as opposed to the controller simply not working).