"Claude writes, Codex reviews" has shown huge promise as a pattern for me, so I wrote a Dockerfile and some instructions on how to make that happen for agents, and ended up with https://github.com/pjlsergeant/moarcode
I am spending most of my day in this harness. It has rough edges for sure, but it means I trust the code coming out much more than I did just Claude.
I don't think you need two separate models for this - I get similarly good results re-prompting with Claude. Well, not re-prompting, I just have a skill that wipes the context then gets Claude to review the current PR and make improvements before I review it.
I tried to opposite because claude was not coding as well as codex some additional modules for my codebase and codex could. Then I tried to get claude to read and critique and it got so many fundamentals wrong I was wondering if I am using the wrong model.