The main objective of this paper is to assess the efficiency of the European Union’s public sector from a quality of governance approach, employing a two-step methodology. In the first stage, EU states’ efficiency scores are determined using Data Envelopment Analysis. Once quantifying public efficiency, the second step of the methodology examines the determinants of efficiency using a quantile regression estimation technique, with an emphasis on demographic features, corruption, economic freedom, and governmental digitalization. The novelty is provided by the assessment of the public sector’s efficiency and efficacy from a broader approach in order to determine the efficiency scores of European Union countries, as well as the key factors that may impact the public sector’s performance. The main findings, namely that governance quality can be considered an important resource in analysing public performance and that human resources, freedom, democracy, corruption, and digitalization have an impact on efficiency, are important considerations not only for policymakers but also for society, researchers, and the academic community. Reform measures should strive to improve both the technical and democratic components of public institutions in order to more effectively and transparently allocate public resources, while taking into consideration local and national peculiarities.