Yeah, it feels really strange sometimes. Bumping up against something that Codex seemingly can't work out, and you give it to Claude and suddenly it's easy. And you continue with Claude and eventually it gets stuck on something, and you try Codex which gets it immediately. My guess would be that the training data differs just enough for it to have an impact.
But if you want that last 10%, codex is vital.
Edit: Literally after I typed this just had this happen. Codex 5.2 reports a P1 bug in a PR. I look closely, I'm not actually sure it's a "bug". I take it to Claude. Claude agrees it's more of a product behavioral opinion on whether or not to persist garbage data, and offer it's own product opinion that I probably want to keep it the way it is. Codex 5.2 meanwhile stubbornly accepts the view it's a product decision but won't seem to offer it's own opinion!
It's because performance degrades over longer conversations, which decreases the chance that the same conversation will result in a solution, and increases the chance that a new one will. I suspect you would get the same result even if you didn't switch to a different model.
They just have different strengths and weaknesses.
which is analogous to taking your problem to another model and ideally feeding it some sorta lesson
i guess this is a specific example but one i play out a lot. starting fresh with the same problem is unusual for me. usually has a lesson im feeding it from the start