An AUC curve that is at least as good as a second curve at all points, is said to dominate it and indicates that the first classifier is equal or better than the second for all plotted values of the parameters, and all cost ratios.
aUC being greater for one classifier than another does not have such a property -indeed deconvexities within or intersections of ROC curves are both prima facie evidence that fusion of the parameterized classifiers will be useful (cf.