Fundamentally there is nothing that unusual about AMTs - they are small format, generally low-power high frequency transducers. At a given price point, they are a little worse than good dome tweeters, but this can probably be explained by the fact that they are a less mature, more complex technology.
Most of their sound differences can be explained by:
- Size: the radiating area of most AMTs is larger then a dome tweeter. Large size = narrower dispersion
- Distortion: probably not very audible, but if a small AMT is used lower down, it will distort more
- Marketing. AMT's have a distinctive appearance which incentivizes designers to use them. They then need to 'highlight' this technology by running the tweeter a bit hot, or otherwise shaping the frequency response.
In a good design not overly constrained by cost or 'showroom sound', the only factor that really matters is the first. In a 3 way, with a small AMT, the differences between the AMT and a dome will be minimal. In a large 2 way, with a huge AMT, the sound will be somewhat distinctive due to the wide horizontal and narrow vertical radiation. The former is still a viable design, but using a big AMT in a big two way is not really a state of the art design in 2022.
The 'crossover' used doesn't make a difference, really. Same tradoffs with a dome tweeter (or ribbon.) Impedance and stuff like that is different, but that doesn't matter much, or matter at all in an active crossover. Cross low and you get potentially smoother directivity match with a woofer at the expense of higher distortion due to LF excursion for the tweeter. Cross high for more output but greater directivity mismatch.
The narrow dispersion is not a bad thing, and I like the use of AMTs in small monitor speakers such as those from ADAM.
The one potentially unique feature of the AMT is that they are dipoles but I don't know of any commercial speakers using them this way, and the best dipole designs seem to rely on forward/backward facing domes (or various planar drivers.)