Abstract Selective predation may affect interspecific competition between coexisting prey species. Ponto‐Caspian zebra (Dreissena polymorpha) and quagga mussels (Dreissena rostriformis bugensis) have become common components of benthic communities in invaded ecosystems in Europe and North America, where they are exposed to predation by molluscivorous fish. In a pairwise food selection experiment, we examined whether an efficient predator of dreissenids, the common carp (Cyprinus carpio), selects between the two mussel species and, if so, which mussel traits (attachment, shell strength, nutritional value) are responsible for the discrimination. The fish were offered simultaneously the two mussel species in three separate treatments: (1) attached individuals; (2) unattached individuals; and (3) freshly removed soft tissue, as well as in three mussel size classes. The fish consistently selected quagga over zebra mussels, irrespective of mussel size and attachment status, including even soft tissues of both species. The success rate of fish attacks did not differ between the prey species. Smaller mussels were easier to crush and swallow, but more difficult to detach from the substratum. Thus, although interspecific differences in attachment and shell strength existed (small and medium zebra mussels had stronger shells and were more strongly attached than corresponding quagga mussels), these traits did not affect fish preferences. However, the differences in chemical composition of the body—the glycogen content (higher in large quagga vs. zebra mussels) and the caloric content (higher in small and medium quagga vs. zebra mussels)—were responsible for fish selection. The higher predatory pressure on the quagga versus zebra mussel suggests that differential predation is not a likely reason for the displacement of zebra by quagga mussels, currently occurring in many European and North American ecosystems. Thus, this phenomenon must be driven by other traits making the quagga mussel more competitive.