Mostly it's based on preference, what you like more. Then there's a few pro's and cons for both.
Play Station [any system] controllers are my personal preference.
Arcade stick isn't my thing, because of the stick specifically.
It feels more comfortable to use a D-pad than some clunk stick to me. Though I know that with a stick, theoretically, you'd be able to double tap directions easier than with a D-pad. The D-pad is always more accurate for me. So when I'm playing streetfighter and want to do 236236 Fierce I trust the D-pad more than the stick. In SC, it doesn't matter as much. I still have a lot of directional input errors with a Stick in SC.
Buttons. Stick > Pad.
Take Hilde and Zero [in TvC, MvC, or UMvC]. Playing these characters on a pad is near impossible with the default control scheme. I've seen many different map outs just to play button charge characters like these, but only on pads. On a stick it's not so difficult to Hold B and A at the same time while you're using K attacks, then releasing A while you're holding onto K. Or in the case of Zero pressing L [and holding it] M H 6H [hold H release L], L [Hold L, release H] M, H, 6H [Hold H, release L] S, 8 More of the hold/release but in the air now, till you knock'em down then you finally release whatever you were holding last [probably H].
Yeah, complicated button pressing is easier on a Stick. Even the simpler things. On a pad I have buttons mapped as BG, A, AB, and ABK for shoulder buttons. Pressing ABK is a pain in the ass [on a controller, that is]. inputing agA is also obnoxious on a pad.
So, If a stick had a D-pad to use, I'd go for that.
I'd want an arcade stick that had something like the wiimote nun-chuck thing, only a D-pad rather than an analogue. The hit box looks like a decent option.
For, SC, I'd go with a GameCube controller. Normally GC controllers suck sweaty balls in fighting games [ever play capcom vs snk for GC?.. Don't]. The button layout is perfect for SC for some reason or another. Easy to press all combinations of buttons except for GK [and in SCII that didn't even do anything. Now to mention it's not that useful anyway. And if you really needed to taunt you could always set it as Z or one of the triggers].