many society's were matriarchal, Egypt was one that change from matriarchal to patriarchal, when we look at our closes relatives the great apes , the family unit is led by an alpha female , most family action are run by the females and the main male action is sleeping , and occasionally protecting his genetic base.........
as to say being led by women is better I'm not to sure of that , i spent my teens in the UK under the "thatcher" era, but then again as i think about it she wasn't what u really call feminine more "evil" really;
i don't think a matriarchal or patriarchal society is a good idea i think we all have something to contribute , i say lower the age you can vote to teenagers then at least we will see some radical changes within or society's and some ppl who are at least "passionate about how we live and run this world of ours................;;