AH is more or less pretty close to what I feel is an ideal fighting game. Low execution requirements (for the most part), encourages creativity, fast, hella deep and most importantly, fun. A lot of the things I like about SC really.
I would say GG is probably the better game in terms of sheer competitive value. However, AH is simply more fun to play. (For me anyway.)
AH is definitely better than BB though. Which should make sense since the series has been around longer. And while I feel BB still has plenty of potential to grow, I would argue that as of now, any iteration of AH is better than any iteration of BB.