There is very much interest in balancing remote delivered multimedia quality and energy consumption in a heterogeneous wireless network environment. This paper proposes a solution for Energy-efficient Device-differentiated Cooperative Adaptive Multimedia Delivery over wireless networks (EDCAM), a hybrid innovative approach which combines multimedia quality adaptation and content sharing mechanisms to save energy at client devices according to their different characteristics. EDCAM relies on an automatic application-aware device profiling, which is proposed to assess individual device energy constraints. These constraints along with QoS delivery scores are used as metrics for the multimedia delivery quality adaptation. Devices make use of content sharing partners with which retrieve the content cooperatively, reducing the usage of high energy consuming networks and therefore increase the delivery energy efficiency. Simulation tests in a WiFi and LTE-based heterogeneous wireless network environment with increasing number of video flows and users show how the proposed EDCAM solution results in significant improvements of up to 40% in terms of energy efficiency in comparison with three other state-of-the-art solutions, while maintaining the performance of multimedia content delivery and estimated user perceived quality at the highest levels.