It is usually safe, but not ALWAYS, to generalize on tweeter sound based on material in my experience. Admittedly, this isn't going to be the most vast repository of information...but, IMO, metal tweeters have generally been able to be classified as noticeably "brighter" than silk dome tweeters. That said, I generally prefer the brighter sound-executed properly. I don't feel it makes as huge a difference in home audio. My biggest experience in the difference was with car audio-I had MB Quart Reference components up from and 6.5" coaxials in the back with titantium dome tweeters. The front components were the only speakers I have ever had to/wanted to turn down the treble. Luckily, they came with their own variable crossover, so I did just that, and attenuated the high frequencies by -3dB. Big improvement in listenability.
I wonder if I noticed this big difference b/c in car audio, one sits so close to the speakers? Perhaps nearly in the near field?
Anyway, you should still listen to some metal dome tweeters and horn tweeters (I would also seek out some ribbon tweeters if you can) to see if you notice a difference...but if your general consensus after a few listens is that they are still too bright, you can probably safely generalize that they are not for you. This will help you narrow down the selection process and find (hopefully!) your audio nirvana a little sooner. There are an overwhelming number of speakers out there to audition!
Realistically, you don't probably have time to listen to all of them to make the best decision....besides, I'm sure that some on here would tell you to be sure you made the right choice, you would have to listen to everything double blind, etc to remove all bias from the equation (looks, etc could factor into how you "want" the speaker to sound b/c you like how it looks). Not to mention the difficulty of finding the same equipment to listen to it all on if you can't take every pair home, lol.
Side note-I agree with the double blind testing as being the most foolproof way to make an accurate decision. I just think it's extremely difficult for the average person to implement in their everyday busy lives. Best saved after you have it narrowed down to just a couple or three selections I would think.