Well the thing is at least how I see it, Back in the day Arcades in America were big in the 1980s everyone went to the arcades to play your classic fighting games like Street Fighter. Because of this many of the older fighting game community members practically grew up on arcades therefore were more used to playing arcade style.
Thus the fight stick was born, essentially a portable arcade controller. High execution and awkward positioning of the hand on a regular pad controller was difficult or impossible to do high execution combos, because of this many people play the arcade stick as well.
In relation to Marvel vs Capcom 3 it’s really relative and once again not needed, yes I think in the high tier tournament scene you’ll see allot more sticks because that’s what people are more comfortable with and work better with not to mention many competitive fighters do not stick to a single fighting game and sticks may be heavily recommended for other games being so used to the stick players brought it over to MvC3
But Mvc3 is relatively easy to learn game because of it’s mechanics and play style often high execution combos are not usually not present in many characters though it does exist in characters like Dante, Spider-Man, Magneto (Somewhat) and others who are execution heavy. Wesker for example is a very good character who doesn’t need high execution to be deadly, so is Sentinel, Wolverine, Phoenix and Dormmamu. So it depends on who you play and what your more comfortable with if you play Dante a hell lot perhaps get a fight stick. Since many of the cast don’t require a fight stick to execute high damage combos, it’s not really necessary but I digress.
IMO: I do not like the 360 Pad for MvC3, which is why I play a PS3 pad, being that I play some lesser execution characters like my main team Wesker, Dormmamu, Sentinel I don’t need it and am already more comfortable with the pad being that unlike many competitive fighters did not grow up in the 80s when the Arcade scene boomed to where it is almost non-existent in present day America. More or less I play easy execution characters in my other competitive game Soul Calibur (Siegfried and Lizardman).
To directly answer your question of “How much of a difference does it make” bluntly
-MvC3 is generally easy to learn and not execution heavy
-Depends on who you play as
-Depends on what controller-type are more comfortable with.