I do find it refreshing that a larger variety of character types are portrayed positively in anime than they are over here, and that goes for both genders. I get especially tired of western media portraying total dickhead alpha type males as attractive almost exclusively.
And on Max White's last point, it's not just the "unique powers" aspect in and of itself, it's the way it's described in such a crunchy fashion. This is actually one thing I typically DON'T like about anime, is everything to do with "super powers" or the like is governed by rigidly structured rulesets that the show will devote lots of time to explaining and tinkering with. I know lots of people that absolutely love this, and it's something I have never ever seen similarly in a western production.
And to add a couple more reasons
Anime/manga ignore genre boundaries and aim to be genuinely thought-provoking a hell of a lot more often than western media.
There is usually a greater emphasis on establishment and relation of setting to plot and character that is generally ignored in western media. This doesn't just mean the invention of interesting worlds for a story to take place in. It means devoting a few seconds in almost every scene to just observing some ambient noise and background imagery. I find it incredibly enhances immersion, cohesion, and dramatic impact.
Almost forgot... relativistic morals are also a lot more common. Things tend to be more black & white in western media, with villains who exist for no reason other than the good guys need someone to beat up and beating them up is usually the cue for happy ending even if it doesn't make any sense.