codex the model (not the cli) is the big thing here. I've used it in CC and w/ my claude setup, it can handle things Opus could never. it's really a secret weapon not a lot of people talk about. I'm not even using xhigh most of the time.
No, the codex harness is also optimized for the codex models. Highly recommend using first-party OpenAI harnesses for codex.
When you say CC is it Codex CLI or Claude Code?