This article by P. Thomas Schoenemann and colleagues is from earlier this year, but it's worth pointing to as a comparative study of more than just humans and chimpanzees. It includes MRI data from 10 nonhuman primate species, with three to five individuals each! That's a consequential sample in a field where the usual comparison has been with two chimpanzees.
Although the human brain is around three times larger than expected for a primate of our body size, it does not seem to be simply a scaled-up version of a primate brain. Because neural tissue is evolutionarily expensive (for metabolic and maturational reasons), changes in relative proportions in different parts of the brain are likely to be behaviorally adaptive. Thus, determining the various ways in which the human brain is different from nonhuman primate brains is of central importance to understanding human evolution. It is clear that at least some areas of the human brain are proportionately smaller than predicted based on primate scaling trends. For example, the human olfactory bulb is only 30% as large and Brodmann's area 17 (primary visual cortex) only 60% as large as predicted for a primate brain our size. Given that the entire human brain is much larger than predicted overall, at least some areas must therefore be significantly larger than predicted.
One area of particular interest for human evolution is the prefrontal cortex, which mediates such important behaviors as planning, working memory and memory for serial order and temporal information, aspects of language (Broca's area and symbolic behavior), attention and social information processing. To the extent that the human prefrontal cortex is disproportionately large, it would suggest that some combination of these behavioral dimensions were particularly important to our evolutionary history (Schoenemann et al. 2005:242, citations elided).
The result is that the total prefrontal cortex volume is relatively larger (i.e., relative to the size of the brain) in humans compared to other primates, and that this increase is mainly attributable to a great increase in the white matter volume. Gray matter in the brain contains a high proportion of cell bodies, while the white matter contains a high density of axons (the fat sheaths around the axons make them white when bundled together).
An increase in white matter probably means that humans have more connections among neurons in the prefrontal cortex has increased in humans relative to other primates. This increase might also mean greater communication between the prefrontal cortex and other parts of the brain.
What does it mean for human evolution? The discussion throws every cognitive change at the problem, from language to social group size to toolmaking. Possibly all are implicated, either separately or together.
In any event, this is one of the clear volumetric differences between the human brain and those of other primates.
Schoenemann PT, Sheehan MJ, Glotzer LD. 2005. Prefrontal white matter volume is disproportionately larger in humans than in other primates. Nature Neurosci 8:242-252. Full text (subscription)