In Mr Walker's text, Crane is a diffident fellow, somewhat repressed, but an intellectual who believes that scientific methods can help solve crimes and cast aside superstition. He is a noble, dedicated creature. He is obviously afraid at many points in the film, but overcomes his fears to act bravely. Mr Walker's carefully carefully constructed Crane is, in the film, and despite the efforts of Johnny Depp to maintain Crane's dignity, often reduced to a buffoon and a comical character by virtue of all the scenes deleted at some point in the transition from screenplay to screen. There, they will read many scenes that did not make it into the finished film.
Some cuts seem inspired by the urge to economize.
When Crane visits a cave-dwelling female hermit in the woods, she leads him into a darker, scarier cave to perform a ritual. In the film, the trip to the inner sanctum is dropped as, I assume, unnecessary. Also, one whole character is cut out, a cancerous reclusive Indian who lives in the woods, and whom some villagers assassinate under the delusion that he is the Headless Horseman haunting the village. When Crane and his Watson visit the old lady in the cave, they gain her audience because they bring her a remembrance of the Indian, a touching moment even as written down in the cold, schematic form of the screenplay. None of this is to say that Sleepy Hollow isn't effective in its current form.