There is a lot to say about this but I want to zero in on one particular aspect of working with women and that is their competitiveness. I'm speaking generally here, I would say this applies to most women but obviously not all.

Women are competitive in a way that men don't intuitively understand. Men compete to dominate each other; a superior product or service, a demonstration of knowledge. These affirm to us that we are indeed the "alpha". It's silly but it's in our nature. However what we care about is achieving a better result than the other guy. The result is the thing that matters. This is why men work well in teams, because we can incorporate that instinct into a collective goal.

Women have a completely different perspective. For women it is not a question of "What was the result?" but "Who gets the credit?" What matters is being seen by others to have achieved something rather than actually achieving it. Women care more about perception than they do reality. Do men care about being seen by others? Of course, but we care about the usefulness of the thing we've accomplished more. As I said, this is a general observation and is not universally true; I've had many great female co-workers, but is something I noticed nevertheless.