Personally, I hate gamepads. Sore thumbs, impossible for multiple button combos, and less accurate than an arcade stick, flight yoke, or steering wheel. Maybe I just suck at using gamepads, but I've had since the nintendo to practice.
I have much better control with an arcade stick in general. Maybe once in a blue moon, a cheaply built arcade stick (or a broken one) sucks worse than the gamepad. Maybe.
Don't get me wrong, though. I have a PC gamepad, and 3 pads for my DC, and use them too. Pads are smaller and fit in your hand. Usually they are cheaper too.
But if money and desk space were no object, I'd replace all the gamepads I have. Hack them maybe, maybe keep some for my friends who prefer gamepads, but not for me.
So, I think you will get better results with an arcade stick than your gamepad, but it will depend on how good a stick you buy and your personal preferences. I don't do fighting games much, and I am a little bias against gamepads (if you couldn't tell), though.
JM2C