Here we explore variation and similarities in the two best-represented population groups who lived during the Middle Stone Age and Middle Palaeolithic-the Neanderthals and Homo sapiens. Building on approaches such as gene-culture co-evolution, we propose a four-field model to discuss relationships between human cognitive evolution, biology, technology, society, and ecology. We focus on the pre-50-ka phase, because we reason that later admixing between Neanderthals and Homo sapiens in Eurasia may make it difficult to separate them in terms of cognition, or any of the other fields discussed in this paper. Using our model enabled us to highlight similarities in cognition between the two populations in terms of symbolic behaviour and social learning and to identify differences in aspects of technical and social cognition. Dissimilarities in brain-selective gene variants and brain morphology strongly suggest differences in some evolutionary trajectories that would have affected cognition. We therefore suggest that rather than insisting that Neanderthals were cognitively 'the same' as Homo sapiens, it may be useful to focus future studies on Neanderthal-specific cognition that may have been well-developed within their specific context at the time.