Growing up, I made the silly mistake of subconsciously projecting how I felt with how 'other' males much felt too, causing me to believe the differences were pretty much limited to how we reproduce and some other physical differences. In other words, since I personally identified as female then everyone, if they had a choice, would obviously like to reflect that biologically however biology necessitated half of people to be male so reproduction could occur. Behavioral differences I attributed to social obligation (like attending school, going to work... stuff you had to be but not because you wanted to).
Obviously... that view led to much confusion in my interactions and understanding of people until I learned that transitioning was possible during college. Once I realized that people actually could switch over and most did not, I finally was clued in that my feelings were likely the exception not the norm.
In the present, I still don't think there's any overarching all-encompassing differences in our brain structure... after all we are the same species (an early fetus has the full potential to grow into either a complete male or complete female, regardless of which sex chromosomes).
In my opinion, the real difference is one at our very center/core that is the source of our desires, needs, and emotions. Many of these are shared by men and women, such as food, warmth, having friends, while many are a little (or a lot) different between genders including body image, sexuality, power, etc. I would guess that such differences are one of the first things to manifest when we differentiate in the womb and form the basis of our gender identity. Transsexuality is an intersex condition specific to this part of development.