We investigate the relationship between the embodiment of an artificial companion and user perception and interaction with it. In a Wizard of Oz study, 42 users interacted with one of two embodiments: a physical robot or a virtual agent on a screen through a role-play of secretarial tasks in an office, with the companion providing essential assistance. Findings showed that participants in both condition groups when given the choice would prefer to interact with the robot companion, mainly for its greater physical or social presence. Subjects also found the robot less annoying and talked to it more naturally. However, this preference for the robotic embodiment is not reflected in the users' actual rating of the companion or their interaction with it. We reflect on this contradiction and conclude that in a task-based context a user focuses much more on a companion's behaviour than its embodiment. This underlines the feasibility of our efforts in creating companions that migrate between embodiments while maintaining a consistent identity from the user's point of view.