Machine Type Communication (MTC) is gaining an enormous interest among communication industry and academia all around the world. The variety of services offered by MTC is expected to significantly increase the number of MTC Devices (MTCD) on wireless networks. The huge number of MTCD poses several challenges to cellular network operators such as efficient radio resource management, energy efficiency (EE) etc. Two main radio resource management techniques to support MTC over 4G Long Term Evolution (LTE) were proposed in the literature: Group Based Scheduling (GBS) and Time Granularity Scheduling (TGS). In this paper, we compare the EE of GBS and TGS by formulating a general expression for the downlink transmit power by eNodeB. The numerical results show that the GBS is more energy efficient that TGS under given quality of service constraints.