In order to allow for dense spatial reuse in wireless ad hoc networks, multiple access interference must be dealt with. This calls for advanced physical layer techniques, such as multiuser detection (MUD) or power control. However, these techniques can only be efficiently applied to ad hoc networks when they are part of a joint physical layer (PHY) and Medium Access Control (MAC) cross-layer design (CLD). In order to better understand both, the potential but also the limits of handling interference by means of MUD and power control, respectively, in this article we provide a comprehensive comparison between MUD-based and power control-based CLDs. We study the behavior of both approaches in terms of throughput, delay, as well as fairness in scenarios with high and low user densities, respectively. To provide more detailed insight in the interaction between MAC and PHY, we separate for each approach the throughput results into gains achieved solely by the MAC layer and by the PHY layer, respectively. These results highlight, among other aspects, some fundamental disadvantage of power control in distributed environments. We conclude that multiuser-based approaches are significantly more beneficial in ad hoc scenarios than power control-based schemes.