Many studies have shown that collaborative tasks in immersive virtual reality (VR) and augmented reality (AR) environments can enhance collaborative outcomes in learning, training, and game-based contexts. However, the literature offers limited information on how these environments differentially shape social presence and collaborative engagement, particularly among unfamiliar users. This study addresses this gap by examining differences in social presence and collaborative engagement between VR and AR environments for unfamiliar pairs. A between-subjects experiment used an escape room game that featured three collaborative tasks, identically implemented in both VR and AR. The key difference was that the VR experience was stationary, while the AR experience required physical movement between rooms. The study involved 52 participants, divided into VR and AR groups, where two unfamiliar participants were paired into teams to complete the tasks. The results indicate significant differences in collaborative dynamics and user perception between the two environments. Specifically, VR pairs reported a stronger sense of immersion and flow state, whereas AR pairs demonstrated greater contextual awareness and behavioral coordination. Cybersickness measures also differed between conditions; given the locomotion mismatch, this pattern should be interpreted cautiously and not attributed to the environment alone. This finding improves understanding of the impact of immersive environments on collaborative processes and offers insights for designing collaborative XR applications (e.g., training and game-based teamwork), particularly for unfamiliar users.