Whether the cognitive competences of monkeys and apes are rather similar or whether the larger-brained apes outperform monkeys in cognitive experiments is a highly debated topic. Direct comparative analyses are therefore essential to examine similarities and differences among species. We here compared six primate species, including humans, chimpanzees, bonobos, gorillas (great apes), olive baboons, and long-tailed macaques (Old World monkeys) in a task on fine-grained size discrimination. Except for gorillas, subjects of all taxa (i.e. humans, apes, and monkeys) were able to discriminate three-dimensional cubes with a volume difference of only 10 % (i.e. cubes of 50 and 48 mm side length) and performed only slightly worse when the cubes were presented successively. The minimal size discriminated declined further with increasing time delay between presentations of the cubes, highlighting the difficulty to memorize exact size differences. The results suggest that differences in brain size, as a proxy for general cognitive abilities, did not account for variation in performance, but that differential socio-ecological pressures may better explain species differences. Our study highlights the fact that differences in cognitive abilities do not always map neatly onto phylogenetic relationships and that in a number of cognitive experiments monkeys do not fare significantly worse than apes, casting doubt on the assumption that larger brains per se confer an advantage in such kinds of tests.Electronic supplementary materialThe online version of this article (doi:10.1007/s10071-013-0616-0) contains supplementary material, which is available to authorized users.