Okay, nice story if not a huge endorsement... I bet the warrior princess could take on you in arm wrestling.
But generally though, yes men beat women in almost anything competitive.
men beat women in things that require raw strength or power.
The range record at Parris Island for the rifle range is held by a female Marine. Most PMIs tell you that women are better natural marksmen.
Intelligence or wisdom required things there is no competitive edge for either side.
Golfing Gator lies again. Men beat women also in intellectual things like chess and.... voting?
When I was a sophomore in college I beat my boyfriend, Vietnam vet and law student, at chess, despite his bragging to his visiting brother that he was going to beat me. Of course I was gentle with him and gave him a special participation award

At voting, we women seem to be much better at it than you guys.