Tabletop interactions can support various social activities such as collaborative review of dynamic sales information in the business setting or route planning with an interactive map among others. Sharing control between users of interactive surfaces can be difficult to ensure participation and efficiency for co-located contexts. We explore the differences between two modalities for interacting with a tabletop map including interactions with a voice assistant and tangible interactions with a shape-changing controller. To simulate a shared goal-oriented situation, we use the context of shared autonomous mobility and compare the tangible controller with voice input through simulated tasks of route planning and detours. The findings suggest that the most suitable interaction modality depends on user preferences, scenarios, and contexts. Tangible controls work well for communicating the state of the system and facilitating discussion, while voice can be more pragmatic and task oriented.