I have used both, used my own tracker to track tokens used, and I saw Claude using twice the tokens to accomplish the same complex task codex had.

Claude was slightly faster, though.

Why does this matter? For me, who is coding apps not so much, but if I went through the route of building an app that uses pay-per-use for potential customers I wouldn't touch Sonnet, but would settle with either kimi or gpt nano models as they have the best price per million tokens used. Though again gpt is slower but less system tokens used.