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Wikipedia writes in Lateralization of brain function:
Significant differences between male and female hemispheric rivalry and dominance have been established. Male brains have significantly better global and rivalry efficiency between the hemispheres. Whereas female brains possess considerably better local efficiency within the RHS [right brain hemisphere].
Is that claim well-supported by evidence?
It is not quite that clean cut. Here is what a 2013 study found:
In the cerebrum, males tend to have greater within-hemisphere connectivity, and females tend to have greater inter-hemisphere connectivity.
However, this effect is reversed in the cerebellum: males tend to have greater inter-hemisphere connectivity, and females tend to have greater within-hemisphere connectivity.
The study used the following method:
In this work, we modeled the structural connectome using diffusion tensor imaging in a sample of 949 youths (aged 8–22 y, 428 males and 521 females)
Ref: Sex differences in the structural connectome of the human brain - Ingalhalikar, et al.
A 2012 Journal of Neuroscience paper concluded that there are significant differences between males and females in brain structure and:
The number of published studies limited to males remains stunningly and stubbornly high (Zucker and Beery, 2010). Scientific conclusions based on the study of one sex could have limited value in understanding some phenomena in the other sex. Thus, females deserve more study.
This says nothing specifically regarding hemispheres, but does show that there are notable differences yet the field is still evolving.
Getting even more specific, a 2014 meta-analysis on sex differences in brain volumes and densities notes:
At a regional level, males on average have larger volumes and higher tissue densities in the left amygdala, hippocampus, insular cortex, putamen; higher densities in the right VI lobe of the cerebellum and in the left claustrum; and larger volumes in the bilateral anterior parahippocampal gyri, posterior cingulate gyri, precuneus, temporal poles, and cerebellum, areas in the left posterior and anterior cingulate gyri, and in right amygdala, hippocampus, and putamen. Females have on average higher density in the left frontal pole, and larger volumes in the right frontal pole, inferior and middle frontal gyri, pars triangularis, planum temporale/parietal operculum, anterior cingulate gyrus, insular cortex, and Heschl's gyrus; bilateral thalami and precuneus; the left parahippocampal gyrus and lateral occipital cortex (superior division).
