Diversity is generally considered as a goal to be achieved in order to bring the Higher Education (HE) system closer to the needs of society. Conversely, some European countries have not favoured diversification processes in HE; instead, they have preferred to pursue a policy aimed at homogeneity across higher education institutions (HEIs), assuming that this would ensure equity and quality of both education and research. The main argument of this paper is that HEIs perform differently and policies that do not consider differences across HEIs are likely to increase inequalities. We test the hypothesis that HE systems regulated on the basis of equality assumptions may rather develop substantial inequalities. We analyse the case of Italian universities and use indicators of research quality. We find deep inequalities in research performance, which are strongly correlated to geographic location. Moreover, we find that inequalities cannot be explained only by the weakness of the local economic context, since they are also strongly linked to the social context and to the adoption of policy measures that that do not address the peculiar features of the HEIs and the context in which they are located.