This paper studies energy efficient resource allocation for a machine-to-machine (M2M) enabled cellular network with non-linear energy harvesting, especially focusing on two different multiple access strategies, namely non-orthogonal multiple access (NOMA) and time division multiple access (TDMA). Our goal is to minimize the total energy consumption of the network via joint power control and time allocation while taking into account circuit power consumption. For both NOMA and TDMA strategies, we show that it is optimal for each machine type communication device (MTCD) to transmit with the minimum throughput, and the energy consumption of each MTCD is a convex function with respect to the allocated transmission time. Based on the derived optimal conditions for the transmission power of MTCDs, we transform the original optimization problem for NOMA to an equivalent problem which can be solved suboptimally via an iterative power control and time allocation algorithm. Through an appropriate variable transformation, we also transform the original optimization problem for TDMA to an equivalent tractable problem, which can be iteratively solved. Numerical results verify the theoretical findings and demonstrate that NOMA consumes less total energy than TDMA at low circuit power regime of MTCDs, while at high circuit power regime of MTCDs TDMA achieves better network energy efficiency than NOMA.