This paper compares the empathetic quality of responses generated by humans and large language models (LLMs). We evaluate four LLMs that were widely used at the time of study—GPT-4, LLaMA-2-70B-Chat, Gemini-1.0-Pro, and Mixtral-8×7B-Instruct—against a human baseline using a large-scale between-subjects study. A total of 1,000 human participants evaluated the empathetic quality of human- and LLM-generated responses to 2,000 dialogue prompts spanning 32 positive and negative emotions. To complement human judgments, we also employed an LLM-as-judge (GPT-4o-mini) to assess the same responses. Across emotions and evaluators, LLM-generated responses were rated as significantly more empathetic than human-written responses. We also observed that both human judges and the LLM-as-judge tended to rate responses generated by their own group more favorably, indicating self-favoring tendencies. These findings highlight both the strong performance of contemporary LLMs in empathetic responding and the need to interpret human- and LLM-based evaluations with care.