Human brains do not look very different from chimp brains yet produce wildly different capabilities.

Judged against neuroscientific and comparative-anatomy consensus as of February 2015. True if mainstream evidence shows human and chimpanzee brains share broadly similar structure and organisation (the same major regions, similar cell types and largely shared genes), with differences mainly in size (about 3x larger in humans), proportions and connectivity, while human cognitive capabilities (language, cumulative culture, technology) differ greatly. Mostly true if the broad similarity holds but the claim understates notable differences such as the threefold size difference or expanded prefrontal and association cortex, which experts would call significant, while still agreeing the overall plan is similar. Mixed if expert sources are roughly split on whether the brains are 'not all that different'. Mostly false if the evidence shows the brains differ substantially in ways experts regard as major (not just size), so the claim seriously distorts things. False if the evidence shows the brains are fundamentally different in structure or that the capabilities are not very different.

Set before the research began.

1. E1 Brain Evolution: Mammals, Primates, Chimpanzees, and Humans - International Journal of Primatology Springer (International Journal of Primatology), author C.E. Oxnard · 4 October 2004

   “Our most recent results demonstrate that chimpanzees and humans are especially different from one another, and the difference is not due to size alone.”

2. E2 Brain Evolution: Mammals, Primates, Chimpanzees, and Humans - International Journal of Primatology Springer (International Journal of Primatology), author C.E. Oxnard · 4 October 2004

   “Part of this difference is merely a continuation, from chimpanzees towards humans, of a trend already present across all other primates that relates mainly to neocortical increase.”

3. E3 The Remarkable, Yet Not Extraordinary, Human Brain as a Scaled-Up Primate Brain and Its Associated Cost National Academies Press (NCBI Bookshelf), In the Light of Evolution Vol. VI, National Academy of Sciences · 25 January 2013

   “the human brain is a scaled-up primate brain in its cellular composition and metabolic cost, with a relatively enlarged cerebral cortex”

4. E4 The Remarkable, Yet Not Extraordinary, Human Brain as a Scaled-Up Primate Brain and Its Associated Cost National Academies Press (NCBI Bookshelf), In the Light of Evolution Vol. VI, National Academy of Sciences · 25 January 2013

   “which is fewer than the 28 billion and 33 billion neurons that we have predicted for the chimpanzee and gorilla brains, respectively”

E3, a 2013 National Academy of Sciences chapter, describes the human brain as "a scaled-up primate brain in its cellular composition and metabolic cost, with a relatively enlarged cerebral cortex." That supports the claim that the overall plan is broadly shared. E4 gives a predicted neuron count for the chimpanzee brain, but the quote does not give the human figure needed for a comparison. E1 and E2, from a 2004 comparative-anatomy study, report that human and chimpanzee brains are "especially different" in ways not explained by size alone, though part of the difference continues a primate-wide trend of neocortical increase. Taken together, the evidence supports broad similarity, while the claim understates notable differences such as the enlarged cortex. That fits the "mostly true" criterion, although none of the sources directly addresses the difference in capabilities.