I think the big thing the limited casts of "anime fighters" have over the diverse rosters of MK and SF is that each character fills their own little niche among gamers. Or, a better way to put it, each character is overpowered in what they do best, but they all have various ways of dealing with what the other fighters do best, so it manages to balance out.
One of the big things I've noticed that these games have over traditional fighters is that the individual inputs are simpler. 236+PP is a universally recognized special move here, and as far as inputs go there really isn't anything harder than 41236+PP. What this means is that advanced play is less about being able to execute individual moves, so much as being able to chain your moves together. A basic combo in these sorts of games, then, would be as follows:
L, L, M, H
Then, when you feel comfortable adding aerials to the game:
L, L, M, H, 3H (Launcher), Air L, Air M, Air H
In essence, I consider these games to be much simpler mechanically than the likes of Street Fighter or Mortal Kombat, and because of this simplicity these games can get away with a faster pace without coming across as too overwhelming for complete newcomers to the fighting genre.
That said, I don't claim to be good at fighters, I just happen to really enjoy the "anime fighter" subgenre.
The core and fundamentals don't change much, but I've found that "anime" fighters tend to have more high risk/high reward scenarios in neutral, where a successful hit means hard control of the game, and a whiff means losing all of that control. Quick reactions while blocking are also important, since gatling combos mean less time to think about what's coming next.
When not in neutral, the game's complexity becomes most apparent. Anime fighters generally offer a lot more universal defensive mechanics than SF or MK, and individual characters are given their own unique tools for dealing with those. The larger number of options on both sides offers many more potential interactions, which means both sides need to keep more in mind, even when one side has the advantage.