Social interactions promote well-being, yet barriers like geographic distance, time limitations, and mental health conditions can limit face-to-face interactions. Emotionally responsive AI systems, such as chatbots, offer new opportunities for social and emotional support, but raise critical questions about how empathy is perceived and experienced in human-AI interactions. This study examines how empathy is evaluated in AI-generated versus human responses. Using personal narratives, we explored how persona attributes (e.g., gender, empathic traits, shared experiences) and story qualities affect empathy ratings. We compared responses from standard and fine-tuned AI models with human judgments. Results show that while humans are highly sensitive to emotional vividness and shared experience, AI-responses are less influenced by these cues, often lack nuance in empathic expression. These findings highlight challenges in designing emotionally intelligent systems that respond meaningfully across diverse users and contexts, and informs the design of ethically aware tools to support social connection and well-being.