Classical optimization and learning-based methods are the two reigning paradigms in deformable image registration. While optimization-based methods boast generalizability across modalities and robust performance, learning-based methods promise peak performance, incorporating weak supervision and amortized optimization. However, the exact conditions for either paradigm to perform well over the other are shrouded and not explicitly outlined in the existing literature. In this paper, we make an explicit correspondence between the mutual information of the distribution of per-pixel intensity and labels, and the performance of classical registration methods. This strong correlation hints to the fact that architectural designs in learning-based methods is unlikely to affect this correlation, and therefore, the performance of learning-based methods. This hypothesis is thoroughly validated with state-of-the-art classical and learning-based methods. However, learning-based methods with weak supervision can perform high-fidelity intensity and label registration, which is not possible with classical methods. Next, we show that this high-fidelity feature learning does not translate to invariance to domain shift, and learning-based methods are sensitive to such changes in the data distribution. Finally, we propose a general recipe to choose the best paradigm for a given registration problem, based on these observations.