I think men are accorded more respect generally for what they do than women are. There is gender bias.
That being said, although it pains me to admit it, I tend to find most of the greatest contributions to science, arts, philosophy have been made by men. I think if you pit an individual woman against an individual man, there is not much difference and I am aware of many of the immense contributions of women. But I think if you are talking sheer numbers.
For the sake of argument, I will discount Nobel Prize Winners, which I believe are part of a political process, and other subjective measures. I will also discount IQ scores which may be skewered to math and spatial, don't place as high an importance on verbal intelligence and leave out artistic intelligence.
But if we are talking about innovative contributions...
All that being said, I don't know whether this is attributable to higher intelligence, greater expectations and opportunity, the fact that women's contributions are buried somewhere, the sometimes inherent humility of women that makes them uncomfortable to push their accomplishments forward and to make sure they are credited for their contributions, or perhaps the immense single-handed purpose that men can be capable of at the exclusion of everything else. I'm not sure whether it is the intelligence of men or the psychology of men. I think some men are less fearful of pushing the envelope, pushing boundaries.
Now we will see what happens if the expectations and opportunity for both sexes do become equal, if women aren't afraid to outshine men, and a hundred other inequities are factored in. But to be honest, I do not know what the result will be.
Although, I will say when you get to Renaissance men and women which does not require the singleminded purpose I talked about earlier, I would guess they would be of equal brilliance. Women are good at multi-tasking, multi-expression. The greater the breadth of expression and creation, the less discrepancy there is--this measure being how many things are you good at.
But if you are talking about the average to gifted man and woman,I find no significant difference. And most of us are going to fall into that category. So, as a woman, I wouldn't be too disheartened and if I were a man, I wouldn't get too cocky.