One idea might be to track the relationship between the origins of horror literature and gothic literature and the development of the horror film genre.
Alternatively, you could look at the conventions of each genre - horror films and horror literature. (Whether we're talking about writing or film, horror is a convention driven genre. The same tools and tropes are used from work to work, e.g., dramatic irony is used heavily in horror where the audience knows something a character does not know.
There is a highly controlled flow of information often used in horror writing, which helps to build tension. Film follows this convention as well, but does it differently.)
Some questions you could try to answer with research:
Does horror writing use the same methods of characterization as horror films? The same methods of creating tension? Seek to create the same emotion, tone, dramatic effect?
Or, you might look at a single writer of horror like Poe or Lovecraft and research their influence on specific directors and writers of horror films or research the relationship between these author's and particular films.
If you are going to look only at film, you might research the differences between original films and the eventual remakes of those films. In this way you can look at how horror films have changed generally and look also at what has remained the same.