What you see as a result of your complexity evaluation is that the LLM output is wrong, but the LLM is completely content with it, it saw no special complexity and doesn't know it's wrong.
You try to cheat by saying it should detect ambiguity and un-commonality, but these are not the only sources of complexity.
For example, after 19:00 sometime (GMT+1), the response quality of both OpenAI and Anthropic (their hosted UIs) seems to drop off a cliff. If I try literally the same prompt the around 10:00 next morning, I get a lot better results.
I'm guessing there is so much personalization and other things going on, that two users will almost never have the same experience even with the same tools, models, endpoints and so on.
You say the outputs "seem" to drop off at a certain time of day, but how would you even know? It might just be a statistical coincidence, or someone else might look at your "bad" responses and judge them to be pretty good actually, or there might be zero statistical significance to anything and you're just seeing shapes in the clouds.
Or you could be absolutely right. Who knows?
I’m already telling Claude to ask Codex for a code review on PRs. or another fun pattern I found is you can use give the web version of Codex an open ended task like “make this method faster”, hit the “4x” button and end and up with four different pull requests attacking the problem in different ways. Then ask Claude to read the open PRs and make a 5th one that combines the approaches. This way Codex does the hard thinking but Claude does the glue
This isn't an exaggeration either. Codex acts as if it is the last programmer on Earth and must accomplish its task at all costs. This is great for anyone content to treat it like a black box, but I am not content to do that. I want a collaborator with common sense, even if it means making mistakes or bad assumptions now and then.
I think it really does reflect a difference in how OpenAI and Anthropic see humanity's future with AI.