In this paper, we examine the error performance of backscatter communication in the presence of ambient interference, where the backscatter device acts as a relay. Specifically, the performance comparison of amplify-and-forward (AF) and decode-and-forward (DF) backscatter relaying is considered for the first time. Considering energy-based detection for on-off keying (OOK) modulation, we derive the statistics of the received signal power, from which the detection thresholds and corresponding bit error rates (BER) are obtained analytically. For the DF scheme, we allow the source node to transmit continuous-wave signals during the relay-to-destination transmission phase to power the backscatter relay. Under a total power budget constraint at the source, we optimize the power allocation for the transmissions in the source-to-relay and relay-to-destination phases. Numerical analysis shows that the DF scheme with optimal power allocation performs similarly compared to the AF scheme, despite the added complexity of the decoding operation. On the other hand, the AF scheme significantly outperforms the DF scheme when the reflection coefficients at the backscatter device do not correspond to perfect OOK. These results provide valuable insights into the design and deployment of backscatter nodes with the goal of improving coverage.