Suppose we train two models on a training set, and then test them both on the training set itself, and on a test set. We have some accuracy metric we're using to evaluate them.
Both models score equally on the test set. However, one model scores higher on the training set than the other. (Assume they both score higher on the training set than on the test set.) Without knowing anything else, is the model whose training and test results are closer together a better model? It seems like it is overfitting less.
If we're looking only to have the model that generalizes best when predicting new data, it seems like both should be considered equally good. Yet, my intuition tells me that I prefer the one whose train and test scores are closer together, though I can't confidently think of a convincing reason for this. Is there any reason to believe that one is better than the other?