Discriminative and generative models approach supervised learning differently, each with distinct advantages. Generative models learn the joint probability distribution, P(X, Y), and can be used when there are hidden variables. They often converge to the true model faster as the sample size increases. In contrast, discriminative models directly learn the conditional probability, $P(Y|X)$, or a decision function, $f(X)$. This direct approach to prediction often yields higher accuracy, as it allows for flexible feature definition and data abstraction, simplifying the learning process when the goal is solely prediction.