AMTs without waveguides or dampening measures applied, pretty much behave like a rectangular diaphragm area producing an even wavefront (similar to a truly pistonic driver without surround). So taller means more pronounced vertical directivity kicking in a bit lower, but would not affect horizontal radiation pattern.
Again, such behavior of inherently increasing directivity is vastly depending on the width of the diaphragm area. An AMT of identical dimensions would always behave like this.
I agree in theory, but practically many of the bigger AMTs show a continuously narrowing radiation pattern in both planes over a broad frequency range which leads to a continuously increasing D.I. at overly high rates. This, on the other hand, makes the lowest band, which shows a relatively wide dispersion, pretty much overrepresented in the room, which I see as a reason for the typical ´analytic´ sound of some AMT-equipped speakers. In the Elac example, this is visible between 4-6K and rather mild.
While I am convinced that AMTs are the most transparent, best-sounding highly directional tweeters in theory, i personally do not like speakers which highlight a particular frequency band in the indirect sound or show steep imbalance in directivity. So a slim but tall AMT might be a better alternative (as exemplarily seen in FinkTeam KIM) or measures to control lower treble/upper midrange directivity by waveguides, dipoles or alike (which is surprisingly unpopular with AMT-equipped speakers).
Be up for a surprise.
