There’s still a bit nuance to that - in most cases I’ve experienced integrated via API in a third-party app, the results have been mostly underwhelming, as opposed to being used directly, preferably with the configurable contexts. Including GitHub and Microsoft Copilot, various choose-your-AI apps, even corporate chatbots, sentiment analyzers and summarizers I’ve worked with. Asking via ChatGPT or Claude directly has produced more acceptable results to me than via an intermediary.
I’d wager this is something more to do with the system prompts when using ChatGPT or Claude from their respective app. Claude system prompts are publicly available. You “should” get the same quality from their API if you set the same system prompt they use for their app. I haven’t tested this but I think this is the right approach if you want to achieve parity between the two.