ML-enabled systems that are deployed in a production environment typically suffer from decaying model prediction quality through concept drift, i.e., a gradual change in the statistical characteristics of a certain real-world domain. To combat this, a simple solution is to periodically retrain ML models, which unfortunately can consume a lot of energy. One recommended tactic to improve energy efficiency is therefore to systematically monitor the level of concept drift and only retrain when it becomes unavoidable. Different methods are available to do this, but we know very little about their concrete impact on the tradeoff between accuracy and energy efficiency, as these methods also consume energy themselves. To address this, we therefore conducted a controlled experiment to study the accuracy vs. energy efficiency tradeoff of seven common methods for concept drift detection. We used five synthetic datasets, each in a version with abrupt and one with gradual drift, and trained six different ML models as base classifiers. Based on a full factorial design, we tested 420 combinations (7 drift detectors × 5 datasets × 2 types of drift × 6 base classifiers) and compared energy consumption and drift detection accuracy. Our results indicate that there are three types of detectors: a) detectors that sacrifice energy efficiency for detection accuracy (KSWIN), b) balanced detectors that consume low to medium energy with good accuracy (HDDM W, ADWIN), and c) detectors that consume very little energy but are unusable in practice due to very poor accuracy (HDDM A, PageHinkley, DDM, EDDM). By providing rich evidence for this energy efficiency tactic, our findings support ML practitioners in choosing the best suited method of concept drift detection for their ML-enabled systems.