As a user of both, Claude's apology is a "sorry I got caught" while Gemini's are more akin to "I'm way out of my debt but I'm really hiding it well". Codex is the only one that seems to acknowledge being wrong in a normal way, yeah I screwed up that's bad I will make a note for it not to happen again.

I wonder how much of that is from their training corpus and how much is from their baked in personnality.