Standard protocols for wireless Internet of Things (IoT) communication must be energy-efficient in order to prolong the lifetimes of IoT devices. Two energy-saving strategies for wireless communication are prevalent within the IoT domain: 1) sleepy devices and 2) radio duty cycling. In this paper, we conduct a comprehensive evaluation as to what types of application scenarios benefit the most from either type of energy-saving strategy. We select the lightweight machine to machine (LwM2M) protocol for this purpose because it operates atop the standard constrained application protocol, and has support for sleepy devices through its Queue Mode. We implement the Queue Mode at both the server side and client side, and design enhancements of Queue Mode to further improve the performance. In our experimental evaluation, we compare the performance and characteristics of Queue Mode with that of running LwM2M in a network stack with the standard time-slotted channel hopping as the duty cycling medium access control protocol. By analyzing the results with the support of an empirical model, we find that each energy-saving strategy has different advantages and disadvantages depending on the scenario and traffic pattern. Hence, we also produce guidelines that can help developers to select the appropriate energy-saving strategy based on the application scenario.