As an American, Claude feels much more natural to me, with the same overly-optimistic "move fast, break things" ethos that permeates our culture. It takes bigger swings (and misses) at harder-to-quantify concepts than Codex, cuts corners (not intentionally, but it feels like a human who's just moving too fast to see the forest for the trees in the moment), etc. Codex on the other hand feels more grounded, more prone to trying to aggregate blind spots, edge cases, and cover the request more thoroughly than Claude. It's far more pedantic and efficient, almost humorless. The dude also claimed that most of the Codex team is European while Claude team is American, and suggested that as an influence on why this might be.
Anyways, I've found that if I force Claude and Codex to talk to each other, I can get way better results and consistency by using Claude to generate fairly good plans from my detailed requests that it passes to Codex for review and amendment, Claude incorporates the feedback and implements the code, then Codex reviews the commit and patches anything Claude misses. Best of both worlds. YMMV
But joking aside, putting it like that I'd think I'd prefer the German/Codex way of doing things, yet I'm in camp Claude. But I've always worked better with teammates that balance my fastidiousness, so maybe that's my answer.