Unpopular Opinion #4:
A matriarchy would not be much different than the patriarchy.
I lived in Germany and speak the language. When I returned to the U.S. I wanted to keep up my language skills and got a lot of books in German. One had the cover off and I don't remember the title but it was written by a woman and was about just that question.
Women were the dominant gender and ruled with an iron hand. Men had to wear PH's (meaning penis holders or jock straps) all the time and if a woman raped a man he would have to be responsible for the child. Men did all the servile work and women were in the military and did the fighting.
When I was in basic training in the military our drill instructor told us he often met with the WAC DI's. He said the stories he heard showed what went on in the women's barracks and the language spoken put the men's side to shame!
So I don't get too many attacks from the feminine side these examples are just what I have read and heard not what I believe.
Eventually, all systems battle corruption. There are always going to be people (male or female) who want more, more, more and the greater good ceases to matter. Sigh...
Different line of hierarchy and succession. I will make war to the queen when pregnant. She won't be able to lead the men into battle unless you are thinking of queendoms were only the females are soldiers. Matriarchy will be different. We may not have too many examples. I know that Elizabeth will be brought and then again there is this rumor and line of thought the real elizabeth died as a child and a playmate boy from her was brought up as Elizabeth and that is why virgin queen never got married and used white makeup to cover beard shade Is one of many theories out there. You have to understand what would had happened to the whole family in charge of elizabeth if she would had died under custody. Her father was not the most compassionate man wearing a crown. Matriarchy would had been different. Hormones, feelings, etc, etc, etc, I am not saying worst I am saying different.