Accuracy and F1-type scores depend on the probability prediction that you choose as the cutoff for assignment of a case into a category. It's quite possible that a change of that cutoff (typically a hidden default of p > 0.5 for binary classification, or the highest predicted probability for a multi-category classification) could affect any of those scores. None of those, however, is a good measure of a model's quality.
AUC is much better in that regard. Although it is not a strictly proper scoring rule, it at least covers the entire range of modeled probabilities rather than depending on a particular cutoff. In your case, neither model gives an AUC significantly different from the value of 0.5 that you get just by chance, so you need to develop yet another model in any event.
In fact, none of the other scores differ significantly from each other between the 2 models, when you take the associated errors into account, so it's not even safe to say that "the first three metrics are better in the first classifier."