I'd argue that Silence of the Lambs as a film is better than the book. Stop here if you want to avoid "spoilers" but I would advise against the time to read the book. The movie is able to cut between scenes more effectively to build tension (specifically the portion where Clarice is ringing Buffalo Bill's doorbell) than a book can. Also, if you take the the films most iconic line, and combine it with what was written in the book, between the two you wind up with the best interpretation.
To provide perspective, Silence is one of three books I'd argue for "better than the book". Fight Club is another and rum is impairing the third. But I know there's a third one.
For this specific concept of in the mind of a disturbed killer, have you read The Shining? For all his faults, this is one of King's best.