Energy consumption is one of the most vital obstacles which face wireless mobile communications to satisfy the User Equipment (UE) with great multimedia services. Unfortunately, the UE battery energy is more absorbed with higher users' requirements. The Discontinuous Reception (DRX) sleep mode is introduced as an energy saving mechanism to turn off the UE radio transceiver circuit when no traffic arrival is indicated from the Base Station (BS). DRX sleep mode can be operated in the Fourth Generation Long Term Evolution (4G LTE) and the Fifth Generation New Radio (5G NR) networks. In 4G LTE DRX networks, the original model is defined as LTE DRX (3-states). In 5G NR networks, the original model is defined as Hybrid Directional-DRX (HD-DRX (4-states)). To enhance the performance, external active states are added to each DRX cycle of the original models. Adding only one active state to the DRX short cycle produces the extended LTE DRX (4-states) and HD-DRX (5-states) models while adding another active state to the DRX long cycle, in addition to the added one to the DRX short cycle, produces the extended LTE DRX (5-states) and HD-DRX (6-states) models. A Semi-Markov chain model is used to describe the UE transition states based on the light traffic threshold value. In this paper, the performance of each extended model is evaluated compared to its original model. Since energy saving and delay are highly trade-offs, the power saving factor and the average delay are the best common metrics to be measured. The extended LTE DRX models enhance the power saving factor by about (0.1 – 9) % compared to that of the original LTE DRX model. The extended HD-DRX models enhance the power saving factor by about (0.2 – 10) % compared to that of the original HD-DRX model. In spite of beam searching process, the extended HD-DRX models reduce the average delay by about (8 – 6000) msec compared to that of the original HD-DRX model. At the end of this paper, there is another performance comparison between the LTE DRX and HD-DRX extended models scenarios.