In multi-LLM RAG system, Is it better to have a separate prompt for each LLM or one prompt for all?

I have a RAG application ( augemented data comes from the web and private documents) that is powered with multiple LLMs, users can click which LLM to use (openai, gemini, claude). In this case, is it better to have a specific prompt for each LLM, or a generic prompt would be better.