I got downvoted for casually mentioning this fact in a subreddit (PurplePillDebate) that supposedly disallows downvotes, so perhaps this needs to be known by more people:

Synapses are the connections between neurons. It turns out, that women, in addition to having smaller brains, have a much lower density of synapses (the number of synapses per unit volume):

http://www.pnas.org/content/105/38/14615/F1.large.jpg (See Figure 1C)

While this doesn't mean that they are dumber than men, the number of synapses places a theoretical limit on the amount of information that can be stored in the brain, and if it wasn't useful to have more synapses, evolution would have kept that number low, to save energy.

Edit Source: http://www.pnas.org/content/105/38/14615.long