Large Language Models (LLMs) have demonstrated remarkable capabilities in conversational tasks. Embodying an LLM as a virtual human allows users to engage in face-to-face social interactions in Virtual Reality. However, the influence of person- and task-related factors in social interactions with LLM-controlled agents remains unclear. In this study, forty-six participants interacted with a virtual agent whose persona was manipulated as “extravert” or “introvert” in three different conversational tasks (small talk, knowledge test, convincing). Social-evaluation, emotional experience, and realism were assessed using ratings. Interactive engagement was measured by quantifying participants' words and conversational turns. Finally, we measured participants’ willingness to ask the agent for help during the knowledge test. Our findings show that the extraverted agent was more positively evaluated, elicited a more pleasant experience and greater engagement, and was assessed as more realistic compared to the introverted agent. Whereas persona did not affect the tendency to ask for help, participants were generally more confident in the answer when they had help of the LLM. Variation of personality traits of LLM-controlled embodied virtual agents, therefore, affects social-emotional processing and behavior in virtual interactions. Embodied virtual agents allow the presentation of naturalistic social encounters in a virtual environment.