Cultural practices can deeply influence genetic diversity patterns. The Neolithic transitions that took place at different times and locations around the world led to major cultural and demographic changes that influenced and therefore left their marks on human genetic diversity patterns. Several studies on the European Neolithic transition suggest that mitochondrial DNA (mtDNA) and Y-chromosome data can exhibit different patterns, which could be owing to different demographic histories for females and males. Archaeological and anthropological data suggest that the transition from hunter-gatherers (HGs) to farmers' societies is probably associated with changes in social organization, particularly in post-marital residence (PMR) rules (i.e. patrilocality, matrilocality or bilocality). The movements of humans and genes associated with these rules can be seen as sex-biased short-range migrations. We developed a new individual-based simulation approach to explore the genetic consequences of 45 different scenarios, where we varied the patterns of PMR and admixture between HGs and farmers. We recorded mtDNA and Y-chromosome data and analysed their diversity patterns within and between populations, through time and space. We also collected published mtDNA and Y-chromosome data from European and Near-Eastern populations in order to identify the scenarios that would best explain them. We show that: (i) different PMR systems can lead to different patterns of genetic diversity and differentiation, (ii) asymmetries between mtDNA and Y-chromosome can be owing to different behaviours between males and females, but also to different mutations rates, and (iii) patrilocality in farmers explains the present patterns of genetic diversity better than matrilocality or bilocality. Moreover, we found that (iv) the genetic diversity of farmers change depending on the HGs PMR rules even though they are assumed to disappear more than 5000 years ago in our simulations.