A common issue for collaborative mixed reality is the asymmetry of interaction with the shared virtual environment. For example, an augmented reality (AR) user might use one type of head-mounted display (HMD) in a physical environment, while a virtual reality (VR) user might wear a different type of HMD and see a virtual model of that physical environment. To explore the effects of such asymmetric interfaces on collaboration we present a study that investigates the behaviour of dyads performing a word puzzle task where one uses AR and the other VR. We examined the collaborative process through questionnaires and behavioural measures based on positional and audio data. We identified relationships between presence and co-presence, accord and co-presence, leadership and talkativeness, head rotation velocity and leadership, and head rotation velocity and talkativeness. We did not find that AR or VR biased subjective responses, though there were interesting behavioural differences: AR users spoke more words, AR users had a higher median head rotation velocity, and VR users travelled further.