In this paper, we investigated a buffer-aided decode-and-forward (DF) wireless relaying system over fading channels, where the source and relay harvest radio-frequency (RF) energy from a power station for data transmissions. We derived exact expressions for end-to-end throughput considering half-duplex (HD) and full-duplex (FD) relaying schemes. The numerical results illustrate the throughput and energy efficiencies of the relaying schemes under different self-interference (SI) cancellation levels and relay deployment locations. It was demonstrated that throughput-optimal relaying is not necessarily energy efficiency-optimal. The results provide guidance on optimal relaying network deployment and operation under different performance criteria.