Directors such as Christopher Nolan and Quentin Tarantino have stated that they oppose digital cinematography due to the inferior image quality. Tarantino even saying that he thinks digital cinema is the "death rattle" of the film industry.
What are the benefits of shooting on film? Pre-2010 it seems film may have had a technical edge, but with the advancing technology I cannot see any way in which film is still superior:
Modern digital cameras are smaller, lighter, cheaper, more flexible and offer a much higher dynamic range, frame rate and a similar or better resolution than their film counterparts. In addition, most films are edited and projected digitally at 2K or 4K which would remove any additional resolution you may gain from film. Even if a "film look" is desired it can be created in post production from digital footage and can look indistinguishable from real film.
Why do many directors and cinematographers still prefer film? I cannot find anything other than vague mentions of "better resolution" or "it just looks better".