The mouthpiece I'm using right now has a wide rim. It's not a deep or shallow cup, but something in the middle.
I tried a few mouthpieces before this one, but this is my favorite. It's very comfortable, easy to play and gives me enough control.
I used smaller mouthpieces when I first started playing, but switched to larger ones as soon as I got the hang of the instrument. I don't think that a small mouthpiece is good except during the beginner phase.