Brain size relative to body size is smaller in migratory than in non-migratory birds. Two mutually non-exclusive hypotheses had been proposed to explain this association. On the one hand, the ‘energetic trade-off hypothesis’ claims that migratory species were selected to have smaller brains because of the interplay between neural tissue volume and migratory flight. In contrast, the ‘behavioural flexibility hypothesis’ argues that resident species are selected to have higher cognitive capacities, and therefore larger brains, to enable survival in harsh winters, or to deal with environmental seasonality. Here, I test the validity and setting of these two hypotheses using 1,466 globally distributed bird species. First, I show that the negative association between migration distance and relative brain size is very robust across species and phylogeny. Second, I provide strong support for the energetic trade-off hypothesis, by showing the validity of the trade-off among long-distance migratory species alone. Third, using resident and short-distance migratory species, I demonstrate that environmental harshness is associated with enlarged relative brain size, therefore arguably better cognition. My study provides the strongest comparative support to date for both the energetic trade-off and the behavioural flexibility hypotheses, and highlights that both mechanisms contribute to brain size evolution, but on different ends of the migratory spectrum.