A MAJOR difference between the DC and arcade versions is the number of inputs that can be buffered. Your average players won't notice this one bit, but high level play riles on something called "Just Frames."
"Just Frames" are moves that will only execute when a commant input is entered during a small window of time (usually just 1-3 frames of animation, hence, just frame). In the arcade version, if I remember correctly, the game can handle up to 1/2 of 254 moves (that is, each player can input 127 commands before the buffer is full, when including null commands to make the full 256).
What difference does it make? Lets assume your opponent is going to juggle you in a match, and one of his commands requires a just frame: mash all your buttons! If you can input 127 commands, it will stop him from getting the just frame. That's really hard, if not impossible, to do... until you try it on a DC.
The DC only allows 62 moves (null + 2 sets of 31). It is a LOT easier to mash out 32 commands.
All that being said, the only time it really matters is in a tournament, and most tournaments use the PS2 version anyhow.
The same problem exists with the DC vs Arcade versions of MVC2 (and, I would assume, all Capcom fighting games).