long term claude code user here, never used cursor, however based on my limited experience, it seems codex can code better than claude code.
here is example of project i worked using codex, it took 10 iterations just to get github actions right https://github.com/newbeelearn/whisper.cpp . you can see the commits made by codex. Project was quite simple it needs to modify whisper to add support for transcribing voice with start/stop keys and copy the transcription to clipboard when stopped. That's it. It performs poorly as compare to CC which gets it right in one shot.
I've been using Codex since before ChatGPT (the OG version) and CC since launch. For me personally - Claude Code with Opus/Sonnet generally has better taste, more personality in interactions, and is more willing to just do the work. Paired with skills, LSPs, linters, and hooks, it works very well. I think of the two like this:
Claude Code with Opus/Sonnet is the L7 senior engineer still gunning for promotion. Hasn't hit burnout, hasn't been ground down by terrible teams yet. Capable and willing to get their hands dirty. Codex (the harness) with GPT-5.4 or 5.3-codex is fantastic but terse. Some of the UX frustrates me. I want a visual task list. That said, Codex as a harness is phenomenal. Think of it as the senior EM / CTO-in-waiting who won't write new code without complaining and nitpicking for hours. But they'll thoroughly tear your code apart and produce a plan you can execute yourself or pass to Claude Code.
Both are great, and so is Factory Droid. Also worth checking out Compound Engineering from Every.to if you haven't.