Men's brains are approximately ten percent larger than women's brains. But proportionate to body size, men's and women's brains actually end up being about the same.
And how about this: studies have shown that male brains are better at mentally rotating an image, like a map, which helps when you're trying to figure out directions. That doesn't mean that female brains are necessarily worse at reading a map.
Other studies have shown that women are generally better at recalling lists of words and phrases. So women might rely more on memory than mental rotation to find their way. Another study showed that men's and women's brains process hearing differently.