While I haven't tried OpenAI for OCR, I've put my small scale OCR work through both Claude and Mistral OCR. Claude is absolutely better - even in OCR work I did last week and compared with Mistral OCR 4.0.
Mistral's one advantage is that Anthropic now flags OCR, because they don't allow anything that could be considered "reproduction", even of work for which you own the copyright. So my new workflow is Mistral OCR for the actual OCR, followed by a proofreading pass by Claude (which is allowed). Claude is obviously more expensive, but it caught entirely hallucinated sentences created by Mistral OCR 4.0, so I was glad for the backup check.
Mistral's one advantage is that Anthropic now flags OCR, because they don't allow anything that could be considered "reproduction", even of work for which you own the copyright. So my new workflow is Mistral OCR for the actual OCR, followed by a proofreading pass by Claude (which is allowed). Claude is obviously more expensive, but it caught entirely hallucinated sentences created by Mistral OCR 4.0, so I was glad for the backup check.