Brendo, the net effects of digital, active cross-overs are about a 3dB improvement in sensitivity, improved imaging, improved soundstage and improved micro and macro dynamics.
The 3dB improvement in sensitivity is a result of the elimination of the traditional analog, passive cross-over. Yes, that's right, half the power you sink into a speaker is turned to heat by the traditional crossover. Put 250W in, 125W of that goes into heating the room as a result of the crossover.
All the other improvements are partly due to much greater control with the spinoroma (family of parametric) curves. The DSP gives the designer a lot of freedom to "flatten this" and "boost that" in a more granular manner. Phase response can also be improved. So can transient response although there is a trade-off there between transient response and frequency response. Then there is also the greater control that an external amp can have over the driver directly with the traditional crossover eliminated.
Your questions about the type of amp and the power required are very good. Axiom I am sure will eventually publish specifications for its driver arrays to make sure that customers can marry them up with their choice of amplification. Or maybe not although that wouldn't be the Ian we know who likes to give customers choice. I suppose Axiom could introduce amps that make the most of their active line and leave the present ADAs to the legacy (analog crossover) speakers. I really believe a new line of amps would make the actives shine even more and that's all I'll say about this publicly. Nothing wrong with the ADAs for the current lines though and in the interim for the actives.
I have no doubt the actives will sound significantly better. I know first hand what havoc analog filters wreak on a design as environmental conditions and part specs (due to tolerances) change. Active filters don't suffer from these limitations. You hear about better crossover parts and all that is true and I've witnessed it on the v4. But, no matter what you do, those parts drift particularly when you're pouring gobs of current into the speaker. If you listen closely, you can hear the effects. That's not your ears objecting to the SPL; that's the speaker objecting as it shifts from its design limits!
Axiom is just starting to scratch the surface with actives. Actives are a geek's haven! Ditto with LFRs.
I'll also add in here that Ian has been obsessed his whole life with eeking the maximum possible performance from his existing driver architecture. No one's told me this - all you have to do is watch what he's been doing and it's pretty darned obvious. That's another reason why he's one of my heroes. I think the actives will open up an entirely new area of research for Axiom. There is stuff happening inside those drivers that actives will naturally expose. I am not saying there's anything wrong with the drivers. I am saying that more knowledge will be gained about how to make them even better. This is the nature of scientific inquiry and the pleasure of finding things out.