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

Too subjective a topic to answer. Too many variables to consider.

Maggie True Ribbon.  no contest.  and i've listened to good examples of Silk dome, Metal, alum, BE, Ring.  honestly i've modified speakers with new tweeters.  i have favored some of the Ring Radiators compared to the dome and they seemed to have better imaging.  BUT nothing compares to a Long Length Dipole Ribbon.  Dipole, dispersion, surface area can't be matched with the other methods. 

If you buy the best example of each type they are all outstanding. So if we look at it in reverse , meaning what is the best cheap tweeter, it boils it down to something more fundamental relating to design. The best inexpensive tweeter is the ring radiator. Even cheap ring radiators perform extremely close the the best examples. 

They really have little character other than transparency and wide dynamics. I have never seen someone say, oh I can hear that ring radiator like they frequently do with metal domes hardness, soft domes smoothing over or ribbon shimmer. 
 

To me the issue is we have become accustomed to hearing a certain signature and have developed a preference for them.

[please excuse my poor English]

IMHO, the AMT (Air Motion Transformer) technology is unquestionably the best of all (when the manufacturer makes it right).

"AMT Air Motion Transformer" is an Oscar Heil patent, now in the public domain. But its quality indeed depends of the implementation that the manufacturer made of the patent. Some cheap AMT tweeters, made in China, weight 660gr and have an uneven frequency response. Other AMT tweeters are made by Mundorf (for instance), weight 1,8Kg, are very linear (and cost more than €1000/piece !!!). So, huge variations here, of course. As with ribbon.

But all technologies confounded, if you take the best of each one, the AMT wins hands down. I attend live acoustic performances, and I wish that my gear to sound like "the real thing". I did not dare to say to Peter Mc Graath (Wilson), while demonstrating a pair of Wilson Alexandria, that I heard just before a better right hand on the piano with an excellent AMT tweeter, powered by Gamut amplification. But I did dare to tell him that such great speakers as Wilsons fully deserved something better than those "nasty" tioxyd titane inverted dome made by Focal (that Wilson used at the time). Luckily, they stopped using them afterwards.

One brilliant use of AMT tweeter is for instance made by French speaker Jean-Marie Reynaud (JMR) Voce Grande ($9000 approx.). Please note that I am NOT French, neither have I any affiliation with JMR! The point is that I recently listen to them twice, and, for the price, I am gobsmacked. I know very few speaker that deliver such a value for the money, if you like speakers that sound very open, and non-fatiguing. And the AMT transducer used plays a big role here. I do not know the origin of the tweeter used in this case, but it is an extremely long model, made of one piece, which covers 1200hz-30000Hz.

Of course, like everyone here, I heard and know very well: soft domes, ribbon (I own a pair of true-ribbon planar ribbon speaker), beryllium, diamond, etc.

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One member said previously:

Tweeter type does not matter. //I respectfully, but emphatically disagree: Yes, it does matter, definitely.

I think many of us have lost hearing in the high frequency ranges.  Depending on the level of hearing loss, some choose brighter tweeters to hear some of the higher frequencies they have lost.  Perhaps, this is why there is such a variety of speaker using different tweeters.  It also depends on the kind of music you listen.  Perhaps, it would be interesting to know what speakers produce the best balanced and neutral sound.  If you listen to classical or operas you are going to want to hear the artist more.