I just posted that and then immediately regretted, since it didn't even answer the question.
But, oh, well.
Though what makes AH movement so great (or at least the most recent version, I don't know if that was there from the beginning) is to have the "dash" command on one button. According to the situation and the direction you input with it, all sort of crazy movement options get opened up, including the most precise system of air homing dash I've seen (and probably amongst the firsts)(at least a game with a ground, not those weird Psychic-Force-like experiments).
The two main benefits are
* because it's a simple press of a button, there's no complex training to simply perform the move like Melee's wave dashing or Tekken's back dash. It's a very complex and precise button, and the amount of possibilities it opens can be paralysing at times, so it's good the command is simple enough even an absolute beginner can perform the movements with a 100% success rate. One can focus on when to use which movement and how to better master the system instead of learning the muscle memory of a tricky cancel.
* it allows for air-to-air battles to be as complex as normal ground-to-ground or air-to-ground battles. That's something that Mahvel-type games struggle with: many things happen in the air, but even with characters with 8-way air dashes are limited in their options compared to what they can do from the ground, so in many cases (not always, of course), when both characters are in the air, the situation remains static until they fall down to neutral: either one is running from each other and the other one tries to catch him, or we're in the middle of a combo, for example. The air movement possibilities in AH are a whole other level of mind games, since it's a universal system. Entire back-and-forth-and-back-again can happen before the characters are back on the ground. That's of course before even you factor character singularities (there are many) and Arcanas.
I really wish other aspects of the game were more to my liking, because mechanically AH is fascinating.
