Bought it when it came out (was a big fan of non-d20 BESM back in the day). Haven't had a chance to play it, but plenty of chances to read through it.
Biggest improvement is the more intuitive "roll high" vs. the older "roll low." There's also a lot of minor tweaks throughout the powers/abilties, and the skill system is no longer prone to the rampant level of abuse that it was under BESM2e.
Generated a bunch of characters a while back (due to being sick as a dog and bored out of my skull), ranging from a mecha jock to a 80's action movie tough guy to a kunoichi, and there were no issues in getting the right feel for the characters.
Darn shame Guardians of Order went belly-up prior to BESM3e's release, as I think they finally got as close to a perfect anima RPG as is humanly possible.