With today’s technology it has become possible to generate and control personalized as well as authentic avatar faces in 3D for social Virtual Reality (VR) applications, as Lombardi et al. [LSSS18] have recently shown. Creating a personalized avatar with facial expressions is expensive in terms of time, computational power and hardware. Against this background, the question arises whether the creation of such a costly avatar with facial expressions is justifiable. A simple, anthropomorphic and generic avatar could be sufficient and probably allows for the same perception of presence. We conducted an initial and brief experiment with 22 participants in two groups and found indications that an arbitrary (in this case a generic) anthropomorphic representation of the dialog partner seems to lead to a lower perception of social presence compared to a personalized representation that resembles the dialog partner. Furthermore, it seems that co-presence is not affected by a personalized avatar. However, further research as well as a more sophisticated experiment design is necessary to finally verify our hypotheses.