This article studies the energy efficiency (EE) of the two-way wireless communication system operating in the full-duplex (FD) and half-duplex (HD) modes, respectively. Particularly, both the residual self-interference (RSI) and power consumption for the self-interference cancellation (SIC) in the FD mode are modeled as linear functions over the transmit power. The EE maximization problems for FD, time-division duplex (TDD), and frequency-division duplex (FDD) modes with the sum and individual spectral efficiency (SE) constraints are studied, respectively. With the sum SE constraint, closed-form expressions for the maximum EE of these three modes are derived, and the maximum EE among them are compared. Based on the comparison results, a duplex selection scheme to achieve the highest EE among the three duplex modes is proposed. With the individual SE constraint, the optimal and suboptimal resource allocation are obtained by utilizing fractional programming for the three duplex modes. Somehow surprisingly, numerical results reveal that the FD mode achieves the best EE performance when the target sum SE or the distance between the two transceivers is relatively large.