This is an old age question.
I have used Titanium, mylar and silk domes, and probably some others.
Here is the frequency response of the beryllium Scanspeak tweeter which is highly touted and used by Focal and Rockport among others.
Here is the same tweeter with a soft dome.
On that basis it would seem the advantage goes to the beryllium.
However lets take a look at another Scanspeak soft dome tweeter I use in my speakers at Eagan.
Here is the SEAS Excel tweeter in my large TLs.
With the exception of the first Scanspeak soft dome example there is a tendency towards smoother response of the soft dome. As to dispersion there is not much in it, with a marginal advantage to soft.
The Beryllium dome has the more extended response out to 20 KHz, the soft domes have good performance to the 15 to 20 KHz range and are 5db down by 20 KHz.
I had a chance to do an extended evaluation of a $21,500 Rockport Atria, that uses that Scanspeak Beryllium dome tweeter. I have to say it was in the main an excellent speaker. However I did feel that it spat at me very slightly. So when I went to look up the tweeter response after, I was not surprised to see that slight roughness from 2 to 6 KHz.
I seem to have used soft domes more than the others, so I suspect I must slightly favor soft domes, but I have no hard and fast feeling about the issue.