Besides the material it is made of, the linearity of the tweeter is also very important. How well the tweeter behaves and how accurate it is, goes a long way to reproducing the sound cleanly without ringing and other artifacts our ears pick up on. Non linearity of the tweeter is much more fatiguing to our brains than the tonal qualities of the midrange or the woofer driver. Where the follies of the midrange or woofer are those we interpret as the nasal or sibilance qualities, bloated or tight bass, the tweeter results in the harshness of the sound much of the time.
Lightness, rigidity and damping are the 3 main factors in a tweeter design. Since the tweeter has to reproduce frequencies in the higher range of the audible bandwidth, it moves at speeds much greater than the rest of the drivers. Obviously for all the micro details to be preserved accurately, the tweeter made of a light, rigid and well damped material is key. Obviously metal dome tweeters, especially the Beryllium which is seven times more rigid than titanium or aluminum and has sound wave propagation three times faster than Titanium and two and a half times faster than Aluminum has an advantage for the acoustical linearity and transparency of the upper end frequencies.
All of which is great unless the music is crappy... Then you hear all that compression and distortion with all the ultra detail of that crap preserved.
