In environments characterized by regional heterogeneity among patches, competitor diversity can enhance ecosystem functions such as biomass production. Studies that have addressed the strength of diversity effects in heterogeneous environments have primarily considered a patchy distribution of resources. However, in many systems, top-down effects influence competitor productivity and composition. We use a three-trophic level consumer-resource model to ask how differential responses to predation influence consumer diversity effects at two scales; 1) in patches with and without predator populations, and 2) at a 'regional' scale, consisting of one patch with- and one patch without a predator population. At the local scale, the strength and direction of consumer diversity effects depended on the strength of the differential response to predation. Positive or negative influences of consumer richness on equilibrium consumer biomass were the result of a selection effect of diversity. At the regional scale, we observed transgressive overyielding driven by a positive complementarity effect for parameters that define a strong differential response to predation. Given the prevalence of spatially and temporally heterogeneous top-down effects on competitor composition in many ecosystems and trophic levels, we advocate consideration of differential predation as an important step towards incorporating realistic trophic complexity into diversity-function studies.