I would like to compare 2 different classifiers for a multiclass text classification problem that use large training datasets. I am doubting whether I should use ROC curves or learning curves to compare the 2 classifiers.
On one hand, learning curves are useful for deciding the size of the training dataset, since you can find the size of the dataset at which the classifier stops learning (and maybe degrades). So the best classifier in this case might be the one reaching the highest accuracy with the smallest dataset size.
On the other hand, ROC curves let you find a point with the right trade-off between between sensitivity/specificity. The best classifier in this case is just the one closer to the top-left part, with the highest TPR for any FPR.
Should I use both evaluation methods? Is it possible for a method with a better learning curve to have a worse ROC curve, and vice-versa?