I think I cant really speak on it much because I really dont know the science, and also given that we dont live in that society yet I have no idea how much improvement would be made, but enough people tell me that the innate physical and hormonal differences exist that I would have to say that at the very top where we are talking born males who have that plus the additional genetics that are required to be the top of any given physical activity would likely stay there.
Where on the spectrum the top women would perform I have no idea, it would be incredibly interesting to see a female phenomenon bridge the gap, and what that would mean for women in general or the gender balance. One thing that I am curious about in these discussion is how we all here talk about women and men and the top level of sports and none of us could likely ever reach that level, I will never be faster than the fastest woman, I imagine given all the training and advantages ill never be faster than the fastest woman, or perhaps even stronger, so when it comes to generalising I dont like to give the impression that "Oh yeah im a man if i put my mind to it I could totally be the best at whatever the best women are". These people, men and women, are so far above me in skill and genetic traits that, frankly, talking about them as "Men/Women" in regards to their prowess always rubs me slightly the wrong way, they are almost in another category of people that are super human.