The main difference between men and women isnt in the amount of some hormones, but in the changes that occur during puberty. At that time, major changes occur in the body of women, to allow them to give birth. Compared to men, they store more fat, build up less muscle, have softer bones and wider hips. All of those are disadvantages in sports, and an adult man will retain them even after hormone therapy.

Here is an article which explains this in more detail than I could