The heterogeneity of the Higher Education (HE) Institutions is one of the main critical issues in the assessment of their performance. This paper adopts a multi-level and multi-dimensional perspective, combining national (macro) and institution (micro) level data, and measuring both research and teaching activity, using performance indicators derived from the European Tertiary Education Register, CWTS Leiden Ranking, and PATSTAT patent database. Clustering and efficiency analysis are combined to characterize the heterogeneity of national HE systems in European countries, and reveal the potential of using micro level data to characterize national level performance. Large differences are observed between the European countries, partially due to the fact that they are in different phases of their scientific (and economic) development and of the re-structuring of their HE systems. Evidence is found that universities specializing either in teaching or in research tend to have a higher efficiency than those institutions balancing research and teaching. Tradeoffs are observed between undergraduate and post-graduate activities, and a “Matthew cumulative effect” seems in place on the European institutions analysed: high quality research is able to attract external funds that stimulate innovative and patenting activities that in turn are self-reinforcing to the scientific activities. The results reveal once more the limits and dangers of one-dimensional approaches to the performance of HEIs.