I think that for myself, I can think of male characters I pigeonhole as much as female ones. The chivalrous one, the not-so-bright muscleman, the mysterious cloaked guy.
I may give female ones a little more leeway, perhaps because I don’t want to give up liking characters that have a little more (possibly somewhat superficial?) identity in common with myself. But even though I acknowledged Yuffie in FF7 as “the annoying one” along with my male gamer friends, I still used her in my party, and I later on I enjoyed finding a fancomic — http://growth.smackjeeves.com/ — expanding on her story, and presenting her as a more well-rounded, interesting, and strong character.
My objective criteria for what makes a great female character in a videogame isn’t much different from what makes a great character, period: realistic, complex, not a flat character, someone I can identify with. I’m not 100% sure what else may sneak into my opinions via my subconscious.
I do, however, find that it’s easier to see a male character as a “default”, all-around average normal hero guy. I think this is true in a lot of media, because there are already so many stories in our culture and history about men being heroes, or pioneers in whatever they do, that when a woman is a hero in the same kind of capacity, it is noteworthy, and that is how you describe her: a FEMALE hero.
It’s in our language, too, whenever we refer to “he” as a default pronoun without thinking about it. Choosing “she” as the anonymous hypothetical person makes the readers notice, whether they appreciate the effort or not: here is someone trying to mix up the status quo in their writing.
Of course, the “someday” goal I’d like to shoot for is to see female heroes being as normal to encounter as male ones.
I think a tough, related question is this: what does it mean to say, “Here is a strong woman”? Is it one who does everything a man does, and better than the average man? Or is it a woman whose strength is tied up in her female-ness? To use examples that are slightly too complex to completely show a distinct difference (but I can’t think of better, offhand): a Zoe (Firefly), or a Sarah Connor (from the chronicles thereof)? Maybe it can be both…