I'm not sure that's the distinction I'd use. To me, it seems more to be a matter of the kind and amount of training data you have.
If you have a ton of labeled data (either for the exact task you're doing, or a related one), DL often wins because it's sufficiently high-capacity to learn sophisticated models from all that data.
On the other hand, if you don't have enough data, then the deep network isn't going to be learnable, in which case hand-tuned methods might do better, depending on how much "domain expertise" you can bake into the system. Faces are a very constrained domain, and since there has been enormous work on them for decades now, it's one area that non-DL algorithms probably still have somewhat of a fighting chance (until people gather & label large enough databases, of course).
If you have a ton of labeled data (either for the exact task you're doing, or a related one), DL often wins because it's sufficiently high-capacity to learn sophisticated models from all that data.
On the other hand, if you don't have enough data, then the deep network isn't going to be learnable, in which case hand-tuned methods might do better, depending on how much "domain expertise" you can bake into the system. Faces are a very constrained domain, and since there has been enormous work on them for decades now, it's one area that non-DL algorithms probably still have somewhat of a fighting chance (until people gather & label large enough databases, of course).