Adjusting for age, on average, they found that women tended to have significantly thicker cortices than men. Thicker cortices have been associated with higher scores on a variety of cognitive and general intelligence tests. Meanwhile, men had higher brain volumes than women in every subcortical region they looked at, including the hippocampus (which plays broad roles in memory and spatial awareness), the amygdala (emotions, memory, and decision-making), striatum (learning, inhibition, and reward-processing), and thalamus (processing and relaying sensory information to other parts of the brain).
When the researchers adjusted the numbers to look at the subcortical regions relative to overall brain size, the comparisons became much closer: There were only 14 regions where men had higher brain volume and 10 regions where women did.
Volumes and cortical thickness between men also tended to vary much more than they did between women. It fits with a lot of other evidence that seems to point toward males being more variable physically and mentally.