In this work, we present a comparative study of two just-in-time (JIT) dynamic bandwidth allocation algorithms (DBAs), designed to improve the energy-efficiency of the 10 Gbps Ethernet passive optical networks (10G-EPONs). The algorithms, termed just-in-time with varying polling cycle times (JIT) and just-in-time with fixed polling cycle times (J-FIT), are designed to achieve energy-savings when the idle time of an optical network unit (ONU) is less than the sleep-to-active transition time. This is made possible by a vertical-cavity surface-emitting laser (VCSEL) ONU that can transit into sleep or doze modes during its idle time. We evaluate the performance of the algorithms in terms of polling cycle time, power consumption, percentage of energy-savings, and average delay. The energy-efficiency of a VCSEL ONU that can transition into sleep or doze mode is compared to an always-ON distributed feedback (DFB) laser ONU. Simulation results indicate that both JIT and J-FIT DBA algorithms result in improved energy-efficiency whilst J-FIT performs better in terms of energy-savings at low network loads. The J-FIT DBA however, results in increased average delay in comparison to the JIT DBA. Nonetheless, this increase in average delay is within the acceptable range to support the quality of service (QoS) requirements of the next-generation access networks.