This question is exactly why the recent controversy about measurements matters so much! The goal of the speaker designer is a flat anechoic response and then they shape to taste from there (with the crossover, not necessarily the drivers). Most modern tweeters are capable of producing the same frequency response regardless of the material used. The reason metal domes are used is because the tend to stay pistonic within a given frequency range allowing the designer to create steeper crossover slopes that match the midrange slope without any dips in the response or introducing distortion or beeming. Any tweeter can be ‘padded’ to reduce its output at a given frequency which to our ears will be interpreted as a ‘softer’ sound. A fabric dome can be boosted in these same regions to sound more sharp/edgy. All this happens in the crossover, not the tweeter driver material. With all that said, metal domes can offer greater detail retrieval because they don’t break up as quickly (staying pistonic longer) as fabric. IMO, most give too much credit for a speakers sound characteristic to the drivers and not enough to the crossover which btw is what the other posters mean when they say ‘implementation’.
soft dome versus hard dome tweeters
As my internet window shopping continues, I was reading on some speakers that listed for the tweeter textile dome and also silk dome.
So then I used the 'search discussion' function on this site on the subject of soft versus hard dome tweeters and it seemed as if most of the members who offered opinions used that "harsh" and "fatiguing" and "ringing" to describe how they felt about hard dome speakers. In the admittedly short time that I spent reading, I was not picking up a lot of love for hard dome tweeters.
But there are reputable speaker manufacturers that seem to have gone the extra mile to make their hard dome tweeters as hard as possible using, for example, beryllium or artificial(?) diamond dust.
I wouldn't expect a consensus on much of anything audio, but did I just by luck to find responses by mostly people who prefer soft dome tweeters? Because if they really sound that bad (harsh/fatiguing/ringing) in comparison, why would reputable manufacturers choose this route? And I do realize that appreciation of a sonic effect is subjective, so did I just happen on responses by members who had mostly the same subjective perception?