There's a certain amount of variance in the way that people utilize these agents. Put five people in a room and ask them to compose the same prompt and you have five distinct prompts. Couple this with the fact that models respond better/worse to certain prompts depending on the stylistic composition of the prompt itself. And since people tend to write in the same style, you'd get people who have more luck with one model over another, where one model happens to align more readily with their prompt style.

To wit, I have noticed that I tend to prefer Codex's output for planning and review, but Opus for implementation; this is inverted from others at work.

I used to feel like you do, but I don't agree. I would just say it is not consistent. For a given codebase and given goal, sometimes Claude will be the more sensible, creative, thoughtful planner and sometimes Codex will be, sometimes Claude will make a serious oversight that Codex catches and sometimes the opposite. But the trend for me and seemingly a lot of people is that Claude is a more "human-like/human-smart" planner than Codex (in a positive way) but is more likely to make mistakes or forget details when implementing major codebase changes.