Many virtual reality (VR) games are based on a first-person perspective (1PP). There are, however, advantages in using another perspective, such as the third-person perspective (3PP). Although there has been some research evaluating the effect of 1PP and 3PP in gameplay experiences, it is largely unexplored for VR games played via the new generation of commercial head-mounted display systems, such as the Oculus Rift. In this research we want to shed some light on the relationship between the different perspectives, when games are played using head-mounted display VR, and simulator sickness, enjoyment, and presence. To do so, we perform an experiment using two different perspectives (1PP and 3PP) and displays (VR and a conventional display) with a popular game. Our findings indicate that 3PP-VR is less likely to make people have simulator sickness when compared with 1PP-VR. However, the former is not perceived as immersive, but this might not be a problem because our data also show that presence is not mandatory for enjoyment. Also, the data suggest that there is no clear preference between 1PP-VR and 3PP-VR for gameplay.