I prefer claude for generation / creativity, codex for bull-headed, accurate complaining and audit. Very rarely claude just doesn't "get it" and it makes sense to have codex direct edit. But generally I think it's happiest and best used complaining.

I have been trying a similar setup since last week using https://rjcorwin.github.io/cook/

I systematically use reviewers agents in Swival: https://swival.dev/pages/reviews.html

Even with the same model (--self-review), that makes a huge difference, and immediately highlights how bad the first iterations of an LLM output can be.