In cognitive radio networks, spectrum sharing among secondary users can benefit from having more transmission opportunities through spectrum handoff. However, the spectrum sharing strategy can also increase negatively the number of performed handoffs. In this work, we study formally the impact of spectrum sharing on spectrum handoff and at the same time the impact of the spectrum handoff on the overall achievable rates from spectrum sharing. We base our study on three proposed spectrum sharing strategies: static, instantaneous and global. We show that depending on the network configuration, static and/or instantaneous can be almost as powerful as the global strategy. In case handoffs are necessary, the global strategy reduces them significantly. Furthermore, we analyze the benefits of multi-channel communications on the quality of sharing in terms of fairness, achieved rate and number of handoffs.