I know that's anecdotal, but it just seems Claude is often the default.
I'm sure there are key differences in how they handle coding tasks and maybe Claude is even a little better in some areas.
However, the note I see the most from Claude users is running out of usage.
Coding differences aside, this would be the biggest factor for me using one over the other. After several months on Codex's $20/mo. plan (and some pretty significant usage days), I have only come close to my usage limit once (never fully exceeded it).
That (at least to me) seems to be a much bigger deal than coding nuances.