For this question I’m referring to sports in which men and women can compete together on equal terms (even if they often don’t). For example, rock climbing would count (if they climb the same rock and are measured by the same metrics), while the hammer throw would not (since men and women throw different hammers). Competitions where score is given out by a jury count too.
Equestrian Sports comes to my mind as the only Olympic Sports where men and women face each other in competitions. Dressage, in particular, is dominated by females. Isabell Werth and Anky van Grunsven are possibly the most prominent ones, having dominated the world class for the last 20 years.
EDIT: I just came across this ESPN article which argues that in shooting, women are consistently doing better than men.