Jen,

A quick note: I grew up in Quincy, MA.

My experience, both in Quincy and after having left, has been the polar opposite. I have found and continue to find (on average) that women are the most competitive, to the point of being counter-productive.

That being said, I find this forum to be the least antagonistic I've ever been associated with. The competition here is generally healthy, everyone trying to help build the better mousetrap (moldy cheese or not).

I'm not convinced that being a project leader has anything to do with gender, or even competition. I think your approach is best: learn to recognize the strengths and weaknesses of team members and let them run with their strengths and offer assistance with their weaknesses. The former requires trust. Trust is the first difficult part of being a manager. Delegation requires trust, without it, a team will fail. The latter requires patience, the second difficulty. A manager who trusts in the skills of the group and has patience with the weaknesses is the one who will succeed.