I think that AIC is the best option, because it is recognized as an index for reporting the trade-off between fitting (likelihood) and parsimony (number of parameters) of the model. It is readily available in R. I think that area under the ROC curves represents just the model fit and should be avoided for comparing models with a different size.

I think that AIC is the best option, because it is recognized as an index for reporting the trade-off between fitting (likelihood) and parsimony (number of parameters) of the model. It is readily available in R. I think that area under the ROC curves represents just the model fit and should be avoided for comparing models with a different size.

Both methods are quite blunt and should not be used to try and tease apart similar models - if two AUC are not significantly different then trying new blunt techniques to discriminate is likely not much use. Use AUROC and AIC to select the most promising models, narrowing the field of what needs more detailed consideration. 

To determine which is more appropriate I am afraid you need to do more detailed work. You should consider risk/ benefit, what the implications of trade offs between true and false positives are. If they are still not significantly different after trade-offs are considered, then considerations go back to practical issues (is one approach more expensive, more complex, more time consuming?). If after all that there is still no discrimination between the models then it doesn't matter.

Since both the AIC and the c-statistic (area under curve) have theoretical basis, albeit each with a different focus, I would be inclined to go with the comparator that provides clearer discrimination between the models. In your case, this would be the AIC.