Tenor or alto? The altos are very mouthpiece friendly. A True Tone tenor however, might give you a hard time on the low end with a high baffled piece.
It really would help to specify tenor or alto.....
No problem on any of the Aristocrat tenors. Of course if you get a "pea shooter" mpc, it might sound shrill no matter what horn you're playing. I like both the Ponzol & RPC baffled mpcs on my Aristocrat tenors.
I have a TT alto and any decent mpc seems to work well on it.
edit: I just realized that an "alto for jazz" was referred to in the original post, so I guess we are speaking altos. My Buescher TT alto is definitely louder, when pushed, than a Yamaha Custom I had for a time. I'm not sure it is edgier, but far more flexible with more of a penetrating sound, not to mention a much better tone, than a Yamaha. No comparison there, really. I don't know about for "rock," but the TT would beat out the Yamaha in a blues setting for sure. With this caveat: I feel any decent sax will work for any type of music with the right mpc. It's more a matter of tone quality and flexibility that separates the wheat from the chaff.