As you subtly pointed out. I think it largely depends on the game itself.
I find games like SFII are easier to play using a joy than most pads because it's far easier to do the "roll" (motions that involve continous changes of the stick such as L->D->R) moves with the stick.
However, I find certain games, such as Super Mario Bros, play better with the most pads because the very very short travel of the pad facilitates instant changes between directions. The button layout plays a role as well since I can use my thumb over two buttons at once. I suppose, it can be argued that the same can be said by using each finger for each button for control.
In the end, I think the deal is what our brains have grown accustomed to on a per game basis (that's the way it is for me). If I originally play the game in the arcade, then my brain wants whatever control was used for that game. If I originally played the game on the console, then it is whatever control was used there.
This is the primary reason I want arcade cabs as part of my collection. I have many of the home versions of the arcade games, but the feel is incrediably different between the two. Conversely, I can't for the life of me figure out why anyone wants to build a console cabinet because those console games have a better playing feel when you're lounging on the couch with soda and chips.
That's just me though.