To me it feels like Claude is more rigid in following the instructions in system prompt which would explain why claude.ai can be a bit annoying at times due to the things you mentioned.

On the flipside if you explicitly permit it to do "bad" things the system prompt, claude is more likely to comply compared to openai's models.

I mainly use only the API version of claude 3.5 and gpt4o. I find no system prompt at all to be preferable over claude.ai / chatgpt.