This is one of those areas where personal preference really comes into play. Metallic dome tweeters tend to produce a "bright" sound. This basically means very accentuated cymbal crashes and in low quality metallic dome tweeters, you'll often get a harsh sound out of them. Silk dome tweeters are much more pleasing to me, and many other people also. As you might guess, good silk dome tweeters prouduce a silky smooth sound. They can't play as high as aluminum or titanium tweeters though, but can usually still play through the entire range of audible tones in most cases.
aluminum highs are generally more harsh than those reproduced by silk drivers. there are, however, a few exceptions to the rule. it's basically a matter of preference. some people like to have there highs extra "crisp" and not as smooth as those provided by silks.
You'll typically get more critical detail out of an aluminum or titanium tweeter, but like said above, they can be harsh if not designed correctly. Most high end metal tweets design the rim to counter resonance and also use a surround that has good damping properties, typically at the expense of efficiency. They also use extremely well designed motor assemblies.
Metal tweets have the same drawbacks that metal mids do. While their resonance occurs past the intended frequency range (usually), you still have harmonics (primarily 2nd and 3rd order harmonics) that can excite the resonance of the cone or dome. In midranges, you can cross the driver around 2 octaves below the resonance to counter this. With a tweeter, this isn't possible since you want it to play to 20khz, and resonance typically occurs around 25khz for a 1" tweeter. That is a big reason why metal tweets have the bad rep instead of metal midranges/midbasses. The main thing out there to counter this harsh sound is to have a superior motor design that has very low distortion. Basically, if you're going to get a metal tweeter, either get a really good one or forget it altogether. A cheap metal dome will sound horrible compared to a cheap silk.
Silks are forgiving, smooth, warmer sounding. They tend to blend better in the vocal region, but also tend to rolloff on top end. Of course, that is a generalization. They can usually be designed to have a lower resonant frequency and because of that, you'll see more of them in systems that require a lower crossover point.
The best of both rival each other very well, it is personal preference in the end. But with metal domes, it's good or bad, not a lot of in-betweens, and unfortunately, most sound bad.