When Codex fits
Use Codex when you want an agent to inspect a repo, make code changes, run checks and hand back an implementation. It is strongest when the goal is a concrete patch.
When Claude Code fits
Use Claude Code or Cowork when the work benefits from careful reasoning, architecture critique, code review, explanation and collaborative implementation planning.
How to test them
Give both the same small repo task with failing tests. Judge whether the result is minimal, idiomatic, verified and easy to review.
Practical recommendation
Use the same prompt in both tools. Judge the result by factual stability, tone, source discipline, structure, actionability, privacy fit and how much human editing remains. A model that wins one task can lose the next.