Hybridization is increasingly recognized as an important evolutionary force. Novel genetic methods now enable us to address how the genomes of parental species are combined in hybrid lineages. However, we still do not know the relative importance of admixed proportions, genome architecture and local selection in shaping hybrid genomes. Here, we take advantage of the genetically divergent island populations of Italian sparrow on Crete, Corsica and Sicily to investigate the predictors of genomic variation within a hybrid taxon. We test if differentiation is affected by recombination rate, selection, or variation in ancestry proportions. We find that the relationship between recombination rate and differentiation is less pronounced within hybrid lineages than between the parent species, as expected if purging of minor parent ancestry in low recombination regions reduces the variation available for differentiation. In addition, we find that differentiation between islands is correlated with differences in signatures of selection in two out of three comparisons. Signatures of selection within islands are correlated across all islands, suggesting that shared selection may mould genomic differentiation. The best predictor of strong differentiation within islands is the degree of differentiation from house sparrow, and hence loci with Spanish sparrow ancestry may vary more freely. Jointly, this suggests that constraints and selection interact in shaping the genomic landscape of differentiation in this hybrid species.