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.
I've seen this with GPT, and I usually ask it to put together a more easy to understand document for a specific target audience or reading level and it seems to do okay.
So claude: 10 paragraphs of prose
codex: 1 paragraph of jargon over jargon.