The growing interest in the self-similarity effect of avatars in virtual reality (VR) has spurred the creation of realistic avatars that closely mirror their users. However, despite extensive research on the self-similarity effect in single-user VR environments, our understanding of its impact in social VR settings remains underdeveloped. This shortfall exists despite the unique socio-psychological phenomena arising from the illusion of embodiment that could potentially alter these effects. To fill this gap, this paper provides an in-depth empirical investigation of how avatars' self-similarity influences social VR experiences. Our research uncovers several notable findings: 1) A high level of avatar self-similarity boosts users' sense of embodiment and social presence but has minimal effects on the overall presence and even slightly hinders immersion. These results are driven by increased self-awareness. 2) Among various factors that contribute to the self-similarity of avatars, voice stands out as a significant influencer of social VR experiences, surpassing other representational factors. 3) The impact of avatar self-similarity shows negligible differences between male and female users. Based on these findings, we discuss the pros and cons of incorporating self-similarity into social VR avatars. Our study serves as a foundation for further research in this field.