Energy sustainability constitutes an important goal for development, as declared at the global and the European levels. Some conditions decisive for energy performance, as suggested by the Environmental Kuznets Curve (EKC) hypothesis, may be specified by the sectoral structure of production, as industries vary in the intensity of energy consumption. Nevertheless, sustainability is not automatically induced along with economic development and it is important to identify its determinants. The aim of the study is to empirically verify whether the sectoral structure of an economy differentiates energy sustainability within 28 European Union member states (the EU-28). To fulfil the task, a static approach was adopted and such taxonomic methods as the Ward agglomeration method and linear ordering based on the Hellwig synthetic measure were used. The hypothesis concerning the essential role of structural features in energy achievements was verified by a one-way analysis of variance. Our results do not confirm the decisive role of economic structure in energy performance for the EU-28 states; however, they suggest some complex relationships. The interference between energy performance and sectoral structure mostly concerned primary and final energy consumptions and energy poverty, as well as the shares of agriculture, industry, traditional services and finance in total production. The findings reveal a need for further research into the potential interlinkages between different dimensions of sustainable development (SD).