I agree with most of the others here, the most important thing is that a character is well written. There are lots of both men and women among my favourite characters.
Thinking over my favourite authors, I find that most of them are women. I'm also somewhat more willing to take a chance on an unkown author -- buying a book based on just one review or a tempting blurb -- if she's a woman. This is mainly because there are a couple of ways to write women badly that I've seen far more often from men than from women:
- Where have all the women gone? Ie. almost no female characters. Any character who could be either a man or a woman just happens to be a man.
- Narrative voice or woman's internal dialogue describes her sexy body, in situations where it's alien and irrelevant. For instance woman walking while thinking about politics, and the author takes the time to describe how her breasts move.
This comes not just from inexperienced and/or blatantly sexist authors -- I've come across this in authors who are otherwise great, and who are outspoken feminists. (Patrick Rothfuss and GRR Martin spring to mind.)
These aren't the only criteria I care about in books, of course. But all other kinds of good and bad writing habits seem to be distributed equally among men and women, at least as far as I've noticed.