In this paper, we systematically study the average rate and outage probability tradeoffs of full-duplex two-way and one-way relaying under residual self-interference. Among various relaying protocols, two common of them are considered: amplify-and-forward (AF) and decode-and-forward (DF). Furthermore, we consider the application of physical-layer network coding (PNC) and analog network coding (ANC) to full-duplex two-way relaying. Novel closed-form expressions for the average rate and outage probability, are presented. The results show that full-duplex two-way relaying can achieve higher rate than one-way relaying in the medium to high signal-to-noise ratio (SNR) region, at the cost of a certain loss in the outage performance. Moreover, DF protocol can achieve better outage performance than the AF one, but it suffers from a certain loss in the rate in the high SNR region. It is also shown that PNC can further improve the rate and outage performance. In addition, the results clearly reveal the effects of time multiplexing, forward protocol, and network coding on relaying systems, which would shed light on designing practical full-duplex relaying schemes.