Edge computing enables data processing closer to the source, significantly reducing latency, an essential requirement for real-time vision-based analytics such as object detection in surveillance and smart city environments. However, these tasks place substantial demands on resource-constrained edge devices, making the joint optimization of energy consumption and detection accuracy critical. To address this challenge, we propose ECORE, a framework that integrates multiple dynamic routing strategies, including a novel estimation-based techniques and an innovative greedy selection algorithm, to direct image processing requests to the most suitable edge device-model pair. ECORE dynamically balances energy efficiency and detection performance based on object characteristics. We evaluate our framework through extensive experiments on real-world datasets, comparing against widely used baseline techniques. The evaluation leverages established object detection models (YOLO, SSD, EfficientDet) and diverse edge platforms, including Jetson Orin Nano, Raspberry Pi 4 and 5, and TPU accelerators. Results demonstrate that our proposed context-aware routing strategies can reduce energy consumption and latency by 35% and 49%, respectively, while incurring only a 2% loss in detection accuracy compared to accuracy-centric methods.