The Message Queuing Telemetry Transport (MQTT) protocol is widely used in IoT applications due to its simplicity and low energy consumption. However, its lack of built-in security mechanisms necessitates the use of additional protocols such as Transport Layer Security (TLS), which introduces overhead that can affect the energy efficiency of constrained IoT devices. This paper presents a quantitative framework for evaluating the trade-offs between security robustness and energy consumption in MQTT-based systems. A methodology is proposed that integrates the Energy Efficiency Index (EEI) and the Security-Energy Cost Ratio (SECR) to assess the impact of various Quality of Service (QoS) levels and TLS encryption on device performance. Experimental measurements were conducted using an ESP32-based testbed with different MQTT configurations. The results indicate that while higher QoS levels improve message delivery reliability, they also lead to increased energy consumption, particularly when combined with TLS. Among all configurations tested, QoS 1 with TLS achieved the best balance between energy efficiency and security, offering practical insights for designing secure and sustainable IoT solutions.