The study of insular populations was key in the development of evolutionary theory. The successful colonisation of an island depends on the geographic context, and specific characteristics of the organism and the island, but also on stochastic processes. As a result, apparently identical islands may harbour populations with contrasting histories. Here, we use whole genome sequences of 65 barn owls to investigate the patterns of inbreeding and genetic diversity of insular populations in the eastern Mediterranean Sea. We focus on Crete and Cyprus, islands with similar size, climate and distance to mainland, that provide natural replicates for a comparative analysis of the impacts of microevolutionary processes on isolated populations. We show that barn owl populations from each island have a separate origin, Crete being genetically more similar to other Greek islands and mainland Greece, and Cyprus more similar to the Levant. Further, our data show that their respective demographic histories following colonisation were also distinct. On the one hand, Crete harbours a small population and maintains very low levels of gene flow with neighbouring populations. This has resulted in low genetic diversity, strong genetic drift, increased relatedness in the population and remote inbreeding. Cyprus, on the other hand, appears to maintain enough gene flow with the mainland to avoid such an outcome. Our study provides a comparative population genomic analysis of the effects of neutral processes on a classical island-mainland model system. It provides empirical evidence for the role of stochastic processes in determining the fate of diverging isolated populations.