It has been shown that, with the instantaneous power constraint and joint power allocation, two-way relaying (TWR) outperforms one-way relaying (OWR) in terms of system throughput. However, the conclusion is not clear for the case with the average power constraint and the case with the instantaneous power constraint but separate power allocation. In this paper, we shall first investigate the optimality of TWR with the average power constraint where we consider both of the joint power allocation among three nodes and the separate power allocation between the source and relay nodes. It will be shown that, with the average power constraint, TWR is not always better than OWR. The conditions with which one scheme outperforms the other are derived and utilized to indicate the operating regions for the two schemes. It is observed that the operating region for TWR, where TWR outperforms OWR, increases as the transmit SNR increases. A similar conlcusion is obtained for the case with the instantaneous power constraint and separate power allocation.