I find codex way more usable. It’s not pretentiously verbose like Claude. It’s also responsive - I can see the progress easily and steer the conversation. With Claude, it might take 15 minutes and I would lose patience.
I held out on OpenAI until last month because I despise Sam Altman, but using Codex is a great experience and 5.5 (medium) I'm on 20$ is very capable, follows instructions when it should and confronts me/challenges me when it should.
UX is nicer where the agent is somehow "separated" from execution.
Both are verbose in their own way, and both - terrible. Claude models love to throw huge blobs of text in architecture planning / interview conversations, but in not a mentally draining language. OpenAI models are more compact, but very dense & formal - they will speak in RFC language for a button that clicks and submits a form.
So claude: 10 paragraphs of prose
codex: 1 paragraph of jargon over jargon.