Using AUC to compare logistic lasso and elastic net

Question

I've seen this question answered here but I do not understand the answer. Harrell recommends using deviance based measures. David Hand (referenced in the thread) says that that the AUC is inappropriate to compare different models, because it uses different misclassifications costs. I don't see how this would be the case when comparing lasso and elastic net, given that they are both trained on the same set of predictors.