In this paper, for cloud-radio access network (C-RAN) architecture which consists of the cloud and base stations (BSs) via dedicated fronthaul link, we investigate the energy efficiency for cloud processing at the cloud and edge processing at each BS. For cloud processing, we reflect the outdated channel state information (CSI) and additional power consumption for the centralized processing. For edge processing, each RRH is allowed to perform baseband processing based on local, but timely CSI. Thus, we reflect the degradation of spectral efficiency induced by inter-cell interference to our energy efficiency model. Furthermore, we propose an RRH selection algorithm for cloud and edge processing to enhance the energy efficiency. Simulation results show that there certainly exists the regime that the edge processing outperforms than the cloud processing. Moreover, we observe that, by means of our proposed algorithm, the energy efficiency is enhanced, especially in cloud processing.