Machine Learning: if test, validation errors are same, the model with lower train loss is better at generalization?
Though usually the test error is your primary goal, I can imagine some specific cases when the train error also matters. One possible example: training set has much more 'hard' inputs than the test set.

If you ever visually examined MNIST, you've probably seen that some images are puzzling even for a human, while others are much easier to tell. If one would split the training/test set differently, it's possible to see that training error would be higher than the validation or test error.

However, it's important to say that a situation like that indicates that data is probably poorly collected or split. So in this case it's better not to choose model A vs model B, but to check the data.