This study examines the effect of prompt engineering on the performance of Large Language Models (LLMs) in clinical note generation. We introduce an Automatic Prompt Optimization (APO) framework to refine initial prompts and compare the outputs of medical experts, non-medical experts, and APO-enhanced GPT3.5 and GPT4. Results highlight GPT4 APO's superior performance in standardizing prompt quality across clinical note sections. A human-in-the-loop approach shows that experts maintain content quality post-APO, with a preference for their own modifications, suggesting the value of expert customization. We recommend a two-phase optimization process, leveraging APO-GPT4 for consistency and expert input for personalization.