Your question was whether there are any physical activities where women can compete with men. You were given one example where women outperform men in a physical activity.
Here are more details of women who had less training than men managed to outperform those men in physical activity.
Here are more details of women who had less training than men managed to outperform those men in physical activity.
http://history.nasa.gov/printFriendly/flats.html
https://en.wikipedia.org/wiki/Mercury_13