The paper investigates the effect of energy taxes in the European Union (EU) across different levels of residential final energy consumption (RFEC) in the period 2005-2016. The analysis is based on quantile panel regression models that directly and indirectly consider energy taxes. More precisely, the developed models provide a multivariate framework for evaluating their effects and, at the same time, for validating the existence of the energy environmental Kuznets curve (EKC) across the selected quantiles. The results unveil significant heterogeneity in the RFEC responses across quantiles. Specifically, in less energy-consuming EU countries, an increase in energy taxes and energy prices influences stronger RFEC, and the rebound effect of real income and tertiary education is greater than in their more energy-consuming peers. Moreover, in the former, the energy EKC hypothesis holds, while in the latter, its existence is not clear, as well as the rebound effect caused by highly educated people. Consequently, EU energy policy aiming at achieving energy and environmental targets has to consider the heterogeneity in RFEC since the outcomes might be different for different energy-consuming groups of countries.