One thing I appreciate with Codex is, OpenAI nowadays sometimes just gives you quota resets you can bank, so when you use up weekly quota before the week ends, you could just reset the quota, to continue using Codex. I've been much less anxious about Codex quota because of this perk. I just used one reset in the bank yesterday, and still have 3 resets left. Whereas with Claude, when you've used 95% quota 3 days before the week ends, you'd be much more anxious.
On the other hand, Claude Code's /remote-control mechanism is extremely helpful when I am running it in the cloud and wants to monitor it or control it on my phone. Codex currently doesn't support this kind of usage. Codex only allows you to use your phone to connect to a session on your desktop, not in the cloud.