I honestly think the average woman is smarter than the average man from my experience. When they talk, they have a much more expansive, detailed, and holistic view of the nuances of events. But I think this also gives them a tendency to read into and react to things that aren't there.
Whereas men speak more to the point, and have more of a tendency to miss relevant information.
Based on what I've read about human evolution, male competition was in hunting skill mainly (the best ones that survived the most got the best mates and thus most surviving offspring), whereas female was in social favor in the group, which requires much more advanced cognition. They had to be a step ahead of everyone socially to get the spot as the first pick of where the tribe's resources go.
Not to mention human intelligence evolved largely based around socializing, and socializing in mammals started with mother-child relationships. So human males through female selection for reliability and nurturing qualities were basically dragged along behind the curve of female social intelligence.
But I think there is a larger subset of males that go to higher extremes of intelligence and creativity, since males were selected for their intelligence. Because someone can be brawny as fuck, but in dangerous prehistoric conditions, that doesn't matter at all if they make shitty tools and suck at using them. Our muscles don't work nearly as well as a chimp's, so skill was a bigger factor than strength. And skill requires intelligence, so the males that went beyond the average intelligence got selected right away. But those are just the above average ones, and social favor still requires more intelligence, since the complexity of social life would evolve with higher intelligence and things like language and whatnot. And the baseline intelligence of the species would raise with more intelligent males having more surviving offspring.