I'm not surprised that people attacked me for saying that I believe there are gender differences.
The fact is that everyone is influenced by their gender, upbringing, personality, DNA, environment and many other factors. It is impossible to tell which factors influence us to what degree and as such there is no real answer to the original question.
It is well documented that there are many differences between males and females, for example men are more mathematical and have better spacial reasoning, while women are more sociable and more nurturing. Of course these differences are harder to pin down in small children.
PlasticCenturion: Yes, I am familiar with that experiment.
There have also been several documented cases of boys born without fully-formed genitalia, who have been raised as girls, either as an accident or as a decision taken by the family, with or without the child knowing the truth.
In many of these cases, the child, even if unaware of being genetically male has expressed unease, discomfort and insecurity about being a girl. Somehow they felt different.
It's difficult to pin down when the differences between girls and boys first appear, but I believe they are, to some extent, hard-wired from birth.