A bit slower? I think for most of my tasks, Claude takes easily 2x longer for almost everything, even things like just analyzing code. It churns tons of tokens for quite simple things.
IMO that's exactly why it's a bit better at actual problem solving.
You absolutely do not "always have to correct" Codex. I'm not sure what you're doing, but I'd say 80-90% of its edits on my side it doesn't need any revisions.