Classical optimization and learning-based methods are the two reigningparadigms in deformable image registration. While optimization-based methodsboast generalizability across modalities and robust performance, learning-basedmethods promise peak performance, incorporating weak supervision and amortizedoptimization. However, the exact conditions for either paradigm to perform wellover the other are shrouded and not explicitly outlined in the existingliterature. In this paper, we make an explicit correspondence between themutual information of the distribution of per-pixel intensity and labels, andthe performance of classical registration methods. This strong correlationhints to the fact that architectural designs in learning-based methods isunlikely to affect this correlation, and therefore, the performance oflearning-based methods. This hypothesis is thoroughly validated withstate-of-the-art classical and learning-based methods. However, learning-basedmethods with weak supervision can perform high-fidelity intensity and labelregistration, which is not possible with classical methods. Next, we show thatthis high-fidelity feature learning does not translate to invariance to domainshift, and learning-based methods are sensitive to such changes in the datadistribution. Finally, we propose a general recipe to choose the best paradigmfor a given registration problem, based on these observations.