Which Tweeter preferred- dome natural material, Beryllium/Metal or Planar Ribbon? Why?

As has been said, any tweeter is only a good as the overall speaker design. The Focal Inverted Ti is a good case in point - a unit that can sound radically different in different applications.

However, purely to expand the field, plasma tweeters e.g. the Lansche unit do have some pretty special qualities.

In mho....I have a pair of the full dipole ESS AMTs that sail away from anything else I've heard in terms of  what you can subject them to....

Get the xover right and pair them to whatever can 'keep up with them' in a space prep'd for dipoles.

Effortless.  And if you overdrive them, the element is replaceable...

(Always thought a line array of them would be scary....)

...but I'm just weird....*L*

There are too many good and bad implementations of each of these materials.  I have heard incredible Beryllium tweeters and painfully bright ones.  I have heard awful diamond tweeters, I have heard brilliant.  Same with ribbons, ceramic, aluminum, AMTs, etc.  There is not best material.  The total system drives the greatness or mediocrity of a speaker.  

Depends, but Magnepan seems to have the best.  The Decca ribbons failed a lot, unfortunately, but maybe they have improved them.

I BELIEVE (don't shoot me if I am wrong, it has been a long time) that the idea is to move as little mass as possible.

Evidently, along with the best (most accurate) speakers on the market, Magnepan has come up with a ribbon-style that is hearty and accurate.  Not bad!

Cheers!

@asvjerry 

Apollo Speakers

https://www.audiogon.com/listings/lisa0ffi-the-apollo-system-high-sensitivity-ob-line-source-amt-based-system-the-apollo-full-range

I would love to hear them.