•We use value-based DEA in the efficiency assessment of structural funds.•We address the specific case of the competitiveness of SMEs across different EU beneficiary regions.•National inefficient programmes mainly need to reduce their dependence on EU co-funding to become efficient.•Almost all inefficient regional programmes need to improve their capacity of execution.•Differences were found on the factors that require adjustments when considering regions’ categories. The funds dedicated to the cohesion policy are aimed at attaining the convergence of wealth levels across the European Union (EU) member states. These constitute the second-highest group of expenditures in the EU budget and thus their evaluation assumes a prominent role. Their assessment can be carried out through different tools and methodologies, all of them with their own merits and flaws. For instance, macroeconomic models allow assessing the potential impact of EU funds on economic growth, but disregard management issues. Other modelling approaches consider direct econometric estimations which might bring biased estimates of the impacts of Structural Funds if some variables are omitted. A different possible tool is Data Envelopment Analysis (DEA), which is a non-parametric method to measure the relative efficiency of Decision-Making Units (DMUs), allowing for the consideration of multiple inputs and outputs in global performance evaluation. In this work we employ the Value-Based DEA approach, which combines DEA with Multiple Criteria Decision Aiding (MCDA) and enables performing a robustness analysis of the results in face of uncertain information, considering the main factors that might influence the efficiency of the implementation of Structural Funds. Specifically, we address the assessment of its application in the competitiveness of small and medium-sized enterprises (SMEs), in different beneficiary regions of the EU. Our analysis helped in the identification of best practices, sources of inefficiency and gaps regarding the benchmark regions/countries, thus leading to shape opportunities for improvement. Overall, we were able to ascertain that national inefficient programmes mainly need to reduce their dependence on EU co-funding to become efficient, whereas almost all inefficient regional programmes need to improve their capacity of execution. Nevertheless, differences were found on the factors that require adjustments when considering regions’ categories.