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.

http://history.nasa.gov/printFriendly/flats.html

https://en.wikipedia.org/wiki/Mercury_13

1. I fail to see women outperforming men on this test. I see them passing the tests - same as men

2. Even if we assume that they outperformed men on the tests, it does not qualify as 'outperforming men in a physical activity'.