Migrant species are commonly thought to be poor competitors in aggressive interactions with resident species. However, no studies have tested if this relationship is widespread. Here we compare the behavioural dominance of closely-related species of migratory and non-migratory birds, testing if migrants are consistently subordinate to resident species in aggressive contests. We compiled published behavioural dominance data involving migrant and resident congeners, gathering additional data on the body mass and migratory distance of each species. Focal species included a diverse array of birds (28 taxonomic families, 12 orders) from around the world. We found that migrant species are usually subordinate to resident species, but that this relationship disappears at larger body sizes. For smaller birds (< 500g), resident species were behaviourally dominant in 83-88% of comparisons; for larger birds (> 500g), resident species were dominant in only 25-30% of comparisons. The relative difference in body mass best predicted dominance relationships among species, with larger species dominant in 80-84% of comparisons. When migrant and resident masses were equal, however, resident species were still more likely to be dominant in smaller birds, suggesting that other factors may also contribute to the subordinate status of migrants. Overall, our results suggest that in smaller species, the evolution of migration is associated with lighter weights and other traits that compromise the competitive abilities of migrants relative to residents. In contrast, larger species appear able to evolve migration without compromising their size or competitive abilities in aggressive contests, suggesting size-dependent constraints on the evolution of migration.