JoyToKey fully supports analog sticks, including multiple axis input. And works perfectly (I'm using a PS2 DS controller). I admit that I haven't bothered with Xpadder, so it ~could~ be better... but I've not had a single problem with JtK and don't see a point in trying something else at this point.
JtK lets you set up multiple profiles, and doesn't take up anything in terms of system resources... but I leave it up to you. I tend to use it for older emulators that refuse to let me use my analog stick or choose buttons myself (Stella X is one of them, the other is AGES because it refuses to accept my controller).
Either way, there are a couple of choices out there so you can re-bind your controls. For me, I wouldn't really suggest mapping your Save/Load state buttons to the controller... because you're likely to hit them by mistake.