I use both. Both are great. But in terms of Desktop Apps I think Codex has the better UI. It's more straightforward, just works, and has small conveniences like the open in editor icon.

Claude's very bloated and convoluted by comparison. Maybe you need the bloat (Claude Design), but I prefer the more razor's edge efficiency of Codex.

Model wise, I can't really tell. They all do what I want them to do most of the time and go off the rails occasionally. The question is increasingly becoming who's faster and cheaper and gives me more tokens, not who's better.