I use opencode, so can toggle between Claude and Codex fairly easily, and do so whenever one of them is having problems (until yesterday, that is, when Claude blocked opencode for good, and I cancelled my account). This means I'm using the same prompts and instructions for both.

Personally, it seems like I have to redirect Opus/Sonnet much less often. GPT felt pretty "dense", it was more likely to ignore earlier instructions in the session, I had to remind it more often, and when I reviewed the code it produced I had to make more corrections that seemed obvious.

Entirely subjective, but I also find I prefer Claude's "personality" to ChatGPT, but I couldn't point to any specific differences.