OMG!!

A shameless plug for my friend Zoe's blog. Zoe has it together and her research, from the beginning of her unexpected self-change from male to female has been deep, wide and thorough. She's an excellent place to begin.
I don't think male/female brains are "shaped" differently, but fMRIs appear to show that different places "light-up" between men and women when similar stimuli are used. In other words we use different parts of our brains in similar circumstances. The major biological differences appear to revolve around vision and how we perceive "field," (men focus on points better and women tend to be field-viewers, it's thought that this may be a result of the long ago division of labor between hunter and gatherer. Hunters require an ability to focus on prey, gatherers require a scanning field-vision in order to be successful.)
Women tend to have better senses of texture and more refined color vision, somewhat more subtle odor-detection systems than do men. Women tend to have a better linguistic capability and more interface between the bi-cameral sides: more cross-information processing between left and right brains.
Men tend to have a larger capacity and women tend to have denser neuronal make-ups: that fact pretty much seems to mean that either can function to the same degree in pretty much all areas. Women tend, psycho-socially to be more attuned to "communion" (feeling/sharing/relationship) and men more attuned to "agency" (doing something about an event.) Women have a different flight/fight response tending to gather and face in response to being startled and also tend to flee more quickly than males. Hormonal changes have been shown to "re-wire" most of these functions and the ways they play-out.
The topic is vast and can be interesting, but it is also a rather infant-study so not a lot is hard and fast as science at present. But differences do appear to be there between sexes, in-born differences, not experientially-derived ones. But there is no one pattern that fits all members of a sex. There is overlap and variation that means that some women are not like most and some men are not like most and in some areas there is so much overlap that no sexual-dimorphism can be drawn at all.
This is not a bad thing, that overlap, instead it is probably an extraordinarily good thing as human beings, mirrored among mammals only by leopards, have the smallest variation betwen individuals in DNA/RNA make-up. In other words, we are all about 99% alike and in comparison to other intra-species variations in other mammals show a huge deal of "inter-bredding" and a rather limited gene-pool from which to derive variation.
Evolution, being driven in large part by a species' variations and how those variations allow continuity and survival in the face of unexpected events called "punctuated equilibrium," places a certain value on differentiation that humans have less than than do chimpanzees and even gorillas, let alone dogs, cats, even elephants.
Nice topic.
Nichole