One of the key elements in The Exorcist's effectiveness is that the film takes itself completely seriously. It approaches the material from a dramatic viewpoint first, and then finds the horror within those situations. The same can be said of The Babadook, a film that understands the value of its characters and their story. By doing so, it infuses the horrific aspects of the film ten-fold, instead of most movies that rely on their scares to create drama. However, it doesn't hurt that the horror elements are equally impressive.
