I don't think OpenAI is training on your data. At least they say they don't, and I believe that. I wouldn't be surprised if the NSA or something has access to data if they request it or something though.
But DeepSeek clearly states in their terms of service that they can train on your API data or use it for other purposes. Which one might assume their government can access as well.
We need direct eval comparisons between o3-mini and DeepSeek.. Or, well they are numbers so we can look them up on leaderboards.