A shorter shaft equates to a short throw in this instance because the joystick itself is so tiny. You can't compensate for a jump with a larger stick, it just takes too much time to rock it back and forth, but you can with the nintendo stick.
I'm sorry your thumbs are slow, most people's aren't.
Most people play track and field on a gamepad with a finger on each button, just like in the arcades. You've been doing it wrong.

Again, I'm not sure what issues you have with your thumb, but I've actually found fighters, even arcade fighters to play BETTER with a d-pad.... it's more accurate then most joysticks... not that it has anything to do with this particular question, I just thought I would mention it since you said so matter of factly that arcade controls are more accurate when in fact they have a lot of "slop" due to their long throws and spring loaded nature. Many people prefer them, myself included, but they are actually less accurate compared to a d-pad. (p.s. Only nintendo does a true d-pad, they have a patent for it. All other companies have to make it slightly different, thus why the d-pad on a 360 controller or psx controller sucks. So when I say d-pad, I'm referring to a nintendo controller.)
There is a black and white answer in this case..... games play differently on different control setups.... this isn't an opinion, it's fact. Now which one you prefer is another story, but odds are, if you are used to playing a game in the arcade you are going to have trouble adjusting to using a gamepad and vice-versa.
My stance has never been that one or the other is better, but rather that the games were deisgned with one control type in mind and if you use the wrong one you are not getting the intended experience. Emulation doesn't end at the software... the interfeace plays a part as well, or else we would all be playing this stuff on our keyboard.