Having played for a long time in now dead arcades and having played for a long time on pad at home too, here are my thoughts on this:
Pad is better at motions, joystick is better at buttons.
I can crank out qcf,qcf much faster on pad than I (or anyone else) can on stick. It’s just faster with a thumb and the shorter motion. I can walk towards you and without you seeing me churning the motion (you’ll see a single instant crouch while I’m walking if even) do a super on pad, I can’t do that on stick. From what I’ve seen in the many many top 8 majors I’ve watched online, neither can anyone else on stick.
On the flip side, stick is better for buttons. On pad you’re usually using your right thumb for the buttons. On stick you’re probably using your index, middle, and ring finger so you have multiple fingers that can manipulate the controls. Not just good for plinking but for holding buttons etc.