So, in what sport-skills can women do as well or better? Endurance? In long distance swimming in cold water, they do better than men. Unfortunately that's not very action-packed--unless you are competing.
Women do as well with a rifle as men, but not as well with a pistol, which is probably due to men's greater strength--they are holding a heavy gun out in the air. With a rifle you have more ways to get the rest of your body involved.
Women don't do quite as well in archery, possibly because men pull heavier bows which means faster arrows which means less wind deflection.
Can somebody think of some competitive events (not subjective, please--no dressage or ice dancing) that aren't speed and strength based?