Biodiversity is well studied in ecology and the concept has been developed to include traits of species, rather than solely taxonomy, to better reflect the functional diversity of a system. The deep sea provides a natural environmental gradient within which to study changes in different diversity metrics, but traits of deep-sea fish are not widely known, hampering the application of functional diversity to this globally important system. We used morphological traits to determine the functional richness and functional divergence of demersal fish assemblages along the continental slope in the Northeast Atlantic, at depths of 300–2,000 m. We compared these metrics to size diversity based on individual body size and species richness. Functional richness and size diversity showed similar patterns, with the highest diversity at intermediate depths; functional divergence showed the opposite pattern, with the highest values at the shallowest and deepest parts of the study site. Species richness increased with depth. The functional implications of these patterns were deduced by examining depth-related changes in morphological traits and the dominance of feeding guilds as illustrated by stable isotope analyses. The patterns in diversity and the variation in certain morphological traits can potentially be explained by changes in the relative dominance of pelagic and benthic feeding guilds. All measures of diversity examined here suggest that the deep areas of the continental slope may be equally or more diverse than assemblages just beyond the continental shelf.