Energy efficiency measures and the deployment of renewable energy are commonly presented as two sides of the same coin—as necessary and synergistic measures to decarbonize energy systems and reach the temperature goals of the Paris Agreement. Here, we quantitatively investigate the policies and performances of the EU Member States to see whether renewables and energy efficiency policies are politically synergistic or if they rather compete for political attention and resources. We find that Member States, especially the ones perceived as climate leaders, tend to prioritize renewables over energy efficiency in target setting. Further, almost every country performs well in either renewable energy or energy efficiency, but rarely performs well in both. We find no support for the assertion that the policies are synergistic, but some evidence that they compete. However, multi-linear regression models for performance show that performance, especially in energy efficiency, is also strongly associated with general economic growth cycles, and not only efficiency policy as such. We conclude that renewable energy and energy efficiency are not synergistic policies, and that there is some competition between them.