If we all of a sudden just handed control of the world over to capable women, I don't know if anything would change. Aside from it being "Mrs. President" and "Mrs. Supreme Dictator" I don't think that the corruption we men are full of would suddenly withdraw its hands. Power gets to anyone, even women, and I actually think women would do a MUCH better job of abusing it than men do. And that's not because I think women are sneaky, it's because I think that women, on the whole, are much more intelligent than men.
However, if we were always controlled by women, I think our societies would be much different. A lot of our history would be changed. For one thing, a lot of our great inventions came about because of people trying to invent helpful war machines. In a world where women rule, we might not have had as many wars. But it's difficult to say, because not every woman is alike. Not every woman is a compassionate, free-thinking caregiver. In fact, some women are downright nasty... even more so than some guys. So who knows. I don't know a lot, so I can't really cite good facts to argue. It's a good question, though.