This is simply the "openness vs directive-following" spectrum, which as a side-effect results in the sycophancy spectrum, which still none of them have found an answer to.

Recent GPT models follow directives more closely than Claude models, and are less sycophantic. Even Claude 4.5 models are still somewhat prone to "You're absolutely right!". GPT 5+ (API) models never do this. The byproduct is that the former are willing to self-correct, and the latter is more stubborn.