Whatever you're most comfortable with.
I know that is not really an answer, but it's true. Personally the only time you would catch me on a stick is if I got stranded in Japan. Otherwise, I've been playing on pad for some 18 years, why throw that away?
As for actual mechanical differences...
On pad, inputting directions is easier/quicker, while button combinations are more difficult. (You can get around this by playing "claw style", or, I like to use my Patented Button Mapping Layout™ so I can play with a standard grip like any other game.)
On stick, button combinations are easier, you can press in any pattern you want without having to do too much hand contortion. But, inputting directions takes more physical effort; you might find some difficulty dashing quickly/inputting double directional inputs (e.g. 66/44). Bro, I hope you lift.
There are fabled reports of the legendary
frankenpad that unites the two forces in unholy matrimony but that's completely ridiculous and unfounded, it probably doesn't even exist...
Of course this is all subjective. Like I said, whatever you wreck shop with, that's what you use. No honor lost in sticking to one camp over the other.