Depending on the type of inputs a game uses, a pad is sometimes easier than a stick. For example, double taps (used for dashing), is actually easier on a pad. Charge motions on the other hand, are much easier on a stick.
Also, I think although a stick gives you more precision, there is a certain point where there are so many directional inputs where it becomes easier to use a pad due to the smaller distance you need to travel. For example, a double fireball motion i believe is easier to do on a pad then on a stick, but that is easily adaptable to with enough practice. If you load the game with constant inputs like double fireballs, I would imagine it would be easier on a pad.
To me, at least, it seems like the main advantage of a stick is the buttons. On a pad, you pretty much have to use your thumb because 2d fighters and claw don't really go together (you usually have to use on of the triggers). It's much easier to time links and combos when you have all of your fingers able to use a natural range of motion. Double tapping for links is also more feasible on a stick. Also, for some reason, if you want to just button mash, it's much more satisfying on a stick, though the only real practical application of that is to mash out of combos, or in games like SC, to mash A and B while guarding so you're more likely to get break a throw.
What it really comes down to though, is what you feel more comfortable with. I've been playing on a stick for so long now, that while I can still play sc on a pad, I find that inputs don't feel as natural anymore and do stupid things because of it. Granted, the only time I played SC in the past 4 months or so was at acen beating random people I didn't know before getting kicked off because the tournament was starting (I didn't enter the actual tournament).
