The X and Z sex chromosomes play a disproportionately large role in intrinsic postzygotic isolation. The underlying mechanisms of this large X/Z effect are, however, still poorly understood. Here we tested whether faster rates of molecular evolution caused by more intense positive selection or genetic drift on the Z chromosome could contribute to the large Z effect in two closely related passerine birds, the Common Nightingale (Luscinia megarhynchos) and the Thrush Nightingale (L. luscinia). We found that the two species differ in patterns of molecular evolution on the Z chromosome. The Z chromosome of L. megarhynchos showed lower levels of within-species polymorphism and an excess of non-synonymous polymorphisms relative to non-synonymous substitutions. This is consistent with increased levels of genetic drift on this chromosome and may be attributed to more intense postcopulatory sexual selection acting on L. megarhynchos males as was indicated by significantly longer sperm and higher between-male variation in sperm length in L. megarhynchos compared to L. luscinia. Interestingly, analysis of interspecific gene flow on the Z chromosome revealed relatively lower levels of introgression from L. megarhynchos to L. luscinia than vice versa, indicating that the Z chromosome of L. megarhynchos accumulated more hybrid incompatibilities. Our results are consistent with the view that postcopulatory sexual selection may reduce the effective population size of the Z chromosome and thus lead to stronger genetic drift on this chromosome in birds. This can result in relatively faster accumulation of hybrid incompatibilities on the Z and thus contribute to the large Z effect.