This letter analytically compares the energy efficiency (EE) between the full-duplex (FD) and the half-duplex (HD) decode-and-forward relaying communications. Different from previous studies, we perform the comparison-based upon a less pessimistic EE analysis for the HD relaying and obtain new insightful conclusions. Specifically, we show that the maximum EE achieved by the FD relaying is always smaller than the HD counterpart if we only impose a relay transmit power constraint. Furthermore, by including a minimum spectral efficiency constraint, the converse is verified true under certain conditions that can be explicitly characterized. The theoretical EE comparison is also supported by simulation results.