I think you should definitely look into more metrics than just AUC and accuracy.
Accuracy (together with sensitivity and specificity) is a very simple but biased metric which forces you to look at the absolute prediction result and does not open for assertion of class probabilities or ranking. It also does not take the population into account which invites to misinterpretation as a model giving a 95% accuracy on a population with 95% chance of being correct at random isn't really a good model, even if the accuracy is high.
AUC is a good metric for asserting model accuracy that is independent of population class probabilities. It will, however not tell you anything about how good the probability estimates actually are. You could get a high AUC but still have very skewed probability estimates. This metric more discriminating than accuracy and will definitely give you better models when used in combination with some proper scoring rule, e.g Brier score as mentioned in another post.
You can get a more formal proof here, although this paper is quite theoretical: AUC: a Statistically Consistent and more Discriminating Measure than Accuracy
There are however a bunch of good metrics available.
Loss Functions for Binary Class Probability Estimation
and Classiﬁcation: Structure and Applications is a good paper investigaing proper scoring rules such as the Brier score.
Another interesting paper with metrics for assertion of model performance is Evaluation: from precision, recall and F-measure to ROC,
informedness, markedness & correlation taking up other good performance metrics such as informedness.
To summarize I would recommend looking at AUC/Gini and Brier score to assert you model performance, but depending on the goal with your model other metrics might suit your problem better.