Superior is going to be subjective and not applicable in all cases.

Right might be a better criterion. A right or correct society is one in which women and men have equal opportunity to choose the kinds of roles and relationships they want to play. It is completely acceptable for a woman to choose to live in a patriarchal relationship in a community where that is the predominate behavior, but it is not acceptable to force or coerce a woman into that relationship or prevent her from escaping that community.

It is not hard to imagine a lot of people being happy conforming to those traditional roles and it is also not hard to imagine many people not wanting to conform to those traditional roles.

Patriarchy, matriarchy or anything in between should be acceptable as long as it is freely chosen and definitely should not be dictated by rule of law.

You should be free to advocate for one approach or the other and claim it is better for the individual or for society in general, but I would oppose any effort to make one form or the other mandatory.

TEK