After training and educating male and female students over many years at public and private institutions for higher learning, I have consistently felt that women are smarter than men.
However, CLAUDE AI begs to differ. On raw cognitive measures, decades of psychometric research find men and women score about the same on general intelligence (IQ), though the shape of the distribution differs slightly, men show somewhat more variance, meaning slightly more men show up at both the very top and very bottom of the range, while women cluster closer to the average. There are also some average differences in specific sub-skills: women tend to edge out men on verbal fluency and reading social cues; men tend to edge out women on spatial rotation tasks. These are small, overlapping differences, not a hierarchy, knowing someone's sex tells you almost nothing about their individual intelligence.
Wisdom is even harder to measure, and there's no solid research showing either sex has more of it. Wisdom tends to track things like life experience, emotional regulation, and perspective-taking, traits that vary enormously within each sex and are shaped far more by upbringing, culture, and individual character than by gender.
If anything, the more interesting research is on how socialization shapes expression, women are often socialized toward more collaborative, relational reasoning, men toward more direct, independent problem-solving — but that's a difference in style, not in capability or wisdom.
Short version: individual variation swamps any average difference between the sexes. Any given man or woman could be wiser or sharper than any given member of the other sex, it comes down to the person.