Teenage girls (and women) love both characters because they embody our fears and our hopes. When we are weak and unable to cope, we want someone in our corner protecting us, especially if he's as perfect as Edward seems to be. We all hope we could summon the inner strength to be the one that does the saving when needed, to be capable of not giving up when life is blatantly unfair. I don't think politics has anything to do with either character’s popularity, but rather it is a matter of the author creating characters that speak to the essence of feminine desires.
Is Katniss really a better role model? For feminists reading the first book in each series, undoubtedly Katniss is closer to their ideal. She is the dominant character, who saves the weaker and nobler Peeta. Bella is the feminine version of Peeta, loving with a persistence that refuses to give in, even though she is the weak one. Ultimately, as Bella’s story develops through the Twilight series, she grows stronger despite her fears and weakness. Her strength becomes manifested as a shield capable of protecting her loved ones from certain destruction.
The power of love is a strong message, as are the hidden strengths of frailty. Where feminists go wrong is in losing sight of the paradox that femininity has embodied throughout the ages: a deep capacity to love and nurture makes the weaker sex more powerful than the man with the club by reminding him of what everyone wants—not dominance, love. That's not a bad message for youth by any standard.