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