The answer to this is that we just don't know.
We do know that there are major differences across cultures in term of what is expected of men and women. This implies that at least some of the differences between the sexes are based on nurture.
Of course, there are significant physical differences between the sexes. The fact that these exist make it at least possible to imagine that there are also mental differences between the sexes. If men and women are physically suited to different things, it might be possible for them to be mentally and/or emotionally suited to different things.
However, we just can't tell. We know that people start treating children differently based on their sex from a very early age. This constant socialization will have a very strong effect on children and make it very difficult to discern what differences in later life are based on nature and which are based on nurture.