We examine how people experience two choices in the design of generative ghosts, AI systems that are trained on data of the dead: representation, where an AI speaks about a deceased person in the third person, and reincarnation, where the AI speaks as the deceased in the first person. Through a qualitative user study with 16 participants, we explore how each shaped authenticity, affect, and risk. Reincarnation was preferred for its immediacy, but participants shared fears of over-reliance. Representation was preferred for engaging with memory over conversational presence, though participants often ignored this distinction, engaging in dialogue despite third-person framing. Across both modes, participants privileged affective resonance over factual fidelity. We conclude by showing how factors such as tone, language, and conversational rhythm -- factors unique to the user's memory of the deceased -- shape interactions with generative ghosts, and argue that those interactions are always collaborative.