First, you cannot determine anything about how women would run the world by those who have had power in the past, from Queen Elizabeth I to Margaret Thatcher. They were operating in a male-dominated world, and they either played by men's rules or didn't play at all.
Then look around you. Can anyone miss the point that men are far more violent than women? Can anyone miss the point that women do 90% of the care taking? These different tendencies result in or reflect different priorities. Men are looking at their power relative to everyone else and becoming aggressive if not violent to protect and increase that power. Women are more likely to be busying themselves building networks, from family reunions to church socials to book clubs to volunteer organizations to children's play groups. Of course, since women live in patriarchal structures, they learn power politics too and can be as ruthless as the men. But, I contend, competition is not as strong an urge in most of us and not the basis on which we build organizations when we are not forced into it by male structures.

What does this tell us about how each gender would run the world? Well, we know how men would run it. They've been doing so for 5000 years and have made a bloody mess of things--war, rape, social stratification, commercial greed, and the near destruction of the planet. All of these problems emerge from the focus on relative power. I think that a change of focus to building communities, fostering individual growth, and protecting the weak--the very things that women have demonstrated their interest in and talent for-- would be a welcome change.

I'm not talking about women having more power than men. It's not an either/or thing. We need to share power. We need to quit denigrating women and their interests and learn from them.