Originally Posted by John P

I'd say use the best tool for the job. But it depends on what you mean by "very different". If you're playing a Bach 1 for legit and a Schilke 6a4a for blowing lead you might run into some problems. With only a couple exceptions, I've always been told to keep the rim pretty much the same and change cup depths depending on what the playing demands are. I play on a Bach 1C for legit and a Curry 1 1/2 Z (essentially a shallow Bach 1 1/2 C) for lead and have no problem switching back and forth between the two of them (not that I would switch them mid-gig). Sure, I could probably get away with using one of the two mouthpieces for everything, but it's unnecessary work. I wouldn't say it's so much about getting high notes, but the SOUND that I try to achieve with lead playing is much different that the sound I go for with legit, and the shallower cup helps me to get the "lead" sound.

There are some other posts on this topic, poke around a bit.