That's interesting, I actively use both and usually find it to be a toss up which one performs better at a given task. I generally find Claude to be better with complex tool calls and Codex to be better at reviewing code, but otherwise don't see a significant difference.
If you want to find an advocate for Codex that can give a pretty good answer as to why they think it's better, go ask Eric Provencher. He develops https://repoprompt.com/. He spends a lot of time thinking in this space and prefers Codex over Claude, though I haven't checked recently to see if he still has that opinion. He's pretty reachable on Discord if you poke around a bit.
Quite irrelevant what factions think. This or that model may be superior for these and those use cases today, and things will flip next week.
Also. RLHF mean that models spit out according to certain human preference, so it depends what set of humans and in what mood they've been when providing the feedback.
Any difference in performance on mobile development?
For that I'm not so sure. I tried both early 2025 and was disappointed in their ability to deal with a TCA based app (iOS) and Jetpack compose stuff on Android, but I assume Opus 4.6 and GPT 5.4 are much better.