Neanderthals brain capacity averaged 1500 cubic centimeters. Modern humans' averaged 1360 cubic centimeters. Why? because Neanderthals were carnivores while homo sapiens were omnivores. Fat babies were the key to the evolution of the large human brain: "High quality diet caused the increse in human brain evolution. Fat and meat and less plant material; in short, a high quality diet has a higher concentration of nutrients and energy. It has been clear for a long time that jaw and tooth structure in modern humans is not designed for heavy or sustained grinding, nor is the modern human gut, especially the colon, designed for digestion and fermentation of large amounts of plant material. Anatomical and fossil evidence shows that as humans modernized, they ate diets that required less grinding and chewing than the diets of other primates. The assumption has been that this occurred because early humans learned how to hunt live game or outsmart other scavengers for animal carcasses." Source: Cunnane, Stephen C. and Michael A. Crawford. " Survival of the fattest: fat babies were the key to evolution of the large human brain." Comparative Biochemistry and Physiology, Part A, 136, 2003. http://www.iugs.ca/File/400/Cunnane_Fattest_CBP_2003.pdf.