Answer:
Model B should be deployed.
Explanation:
(a) I would deploy the model that does well on generalizing well on validation data and does considerably well on training data, Hence, Model B should be deployed because it has less BIAS and the problem of overfitting the training set is evaded.
(b) Model A does well on the training dataset and not very well on test/validation dataset because it has OVERFITTED the training set.
OVERFITTING is a scenario where the model has large variance and low bias, that is has a perfect representation of the training set and performs woefully on generalizing validation set. For instance when a neural network has too much hidden layers and no regularization or dropout.
OVERFITTING is a common scenario in model Development.