I must say that, while this topic is old, at least it's interesting.

In keeping with traditions long since past, I must say that I'm far more for the feminine female as opposed to the heroic heroine when it comes to women. As far as stories go though, I can see it either way.

While, yes, it's true, I'll never applaud tomboys as much as I will damsels, it's the ability for women to be portrayed in both ways effectively that I believe makes them so fascinating. Yes, there's some sexism involved with women being portrayed as weaker characters, but, at the same time, they play their vital roles as everyone else has already mentioned. They're seers, prophetesses, queens, damsels, servants, and even knights.
Though the general consensus may be that men are the stronger and females the weaker, there are literally hundreds of thousands of examples of each gender in a variety of roles. Men do play weaker roles in many stories, and if anyone's ever read anything by Anne McCaffrey (especially the Dragonriders of Pern series) then the whole scope comes out for both men and women, strong and weak, powerful and helpless, hero(ine) and villain, it's all there.

As far as anime goes, it's unfortunate but true, females tend to play weaker roles. It's a societal thing. They're a male oriented society, as most cultures have been for a long while, even though some of us have 'grown out of it.' So, unfortunately, males control the market and what males want to see is, typically, gratuitous panty shots and busty heroines wearing skirts so short they might as well be belts.
Luckily, for those of us guys who don't want to see that and for women alike, the newer animes are, at the very least, trying. I call your attention to Fate/Stay Night and 5cm Per Second, among others which I'm too lazy to list right now.

And... I think this post is long enough. I'll do more when attention is called to it.