I wouldn't know about composites. Aluminum tweeters are the least problematic of the three, since the breakup mode is about at the same frequency as redbook CD bandwidth (22KHz). Mostly its only the younger people that can hear it.
Even if they're the "least" problematic, they will sound the worse if not done correctly. Case in point, the DM 303s are what I expected to walk out with one day. Instead, I got the SuperZero XUs . . . a soft dome which I had actually despised till it compared favorably to my Focals.
Seriously, the 303s were that bad. No decay, felt compressed in the treble. I'd say it was one step away from being your basic entry Klipsch.
But you can't really avoid the resonances in the midrange frequencies, and both the Veritas (discontinued for ages) and the NHT Classic series (arguably a ripoff--I've heart NHT dealers say Veritas "inspired" the design.) both use aluminum for all of its drivers. I've had Axiom speakers before...sold it within a week...felt like my ears were bleeding. Anyway, both are 3-ways that suffer from massive comb filtering, which forced both Energy and NHT to come up with interesting ways to house/block off the two drivers from each other. In the end it probably wasn't worth the tradeoff (imagine having no choice but to listen to speakers with the grills on...that's basically what you're left with).
Once again though, it can change from company to company. The first ones to figure out that anodizing dampens internal resonance wins.
That's what it comes to though. If done right, metal can be a great substance to work with for speakers. If done wrong, anything can sound bad really.