Open-domain conversational QA (ODCQA) calls for effective question rewriting (QR), as the questions in a conversation typically lack proper context for the QA model to interpret. In this paper, we compare two types of QR approaches, generative and expansive QR, in end-to-end ODCQA systems with recently released QReCC and OR-QuAC benchmarks. While it is common practice to apply the same QR approach for both the retriever and the reader in the QA system, our results show such strategy is generally suboptimal and suggest expansive QR is better for the sparse retriever and generative QR is better for the reader. Furthermore, while conversation history modeling with dense representations outperforms QR, we show the advantages to apply both jointly, as QR boosts the performance especially when limited history turns are considered.