If "girls" ruled the world, some "boys" might well be saying "Gag me with a spoon."
If "women" ruled, by analogy with "patriarchy," women's work would be more valued than men's work, e.g., secretaries, nurses, teachers, even homemakers--work that females tend to do--would be paid more than e.g. firefighters, construction workers, etc. (This assumes that the fairness of market-related value of labor is abrogated by sexists of both sexes.)
Matrilineal descent would tend, in less-bourgeois societies, to provide "girls" with more privilege and inheritance than "boys." Matrilocality--the man going to live near the woman's parents--would likewise be the mirror-image of patriarchy.
Note that when women leaders do appear, in modern societies, not too much changes (Indira Gandhi, Golda Meir, Margaret Thatcher, et al.).
For your own information, it is worth noting that women in more 1st world or developed societies are certainly claiming even more than their "fair" (quotas) share (50%) of medical, legal, and other such professions.