On this subject, one of these days I really must do a compare/contrast piece on The Silence of the Lambs and Se7en (spoilers ahead for both films, if you haven't seen them).
I recall reading an interview in Empire magazine with Jonathan Demme when The Silence of the Lambs came out, in which he stated it wasn't a film that invited the audience to cheer at violence. I disagree.
Hannibal Lecter, played with magnetic charm by Anthony Hopkins, may be a cannibal serial killer, but he's also polite, has fine taste in wine, and is cultured, etc, etc. The film does sort of have you rooting for him, especially given his treatment at the hands of the head of the psychiatric institution (whom he later tells Jodie Foster about over the phone, after his escape, claiming "I'm having an old friend for dinner").
On top of all this, the audience with which I saw The Silence of the Lambs literally cheered when the Buffalo Bill killer is gunned down by Jodie Foster in the tense finale. Don't misunderstand me: This is a first-rate thriller with fine performances, but it absolutely is a film that invites the audience to cheer at violence.
By contrast, the serial killer at the heart of David Fincher's Se7en is a scumbag lunatic for whom no pity is felt. Nor is he portrayed as "cool" for being "cultured" any way (as Brad Pitt says, just because he has a library card doesn't make him Yoda). Furthermore, it is difficult to imagine even the most morally depraved of audiences cheering when Brad Pitt finally puts a bullet in his head, for reasons that are obvious to anyone who has seen the film.
Both are excellent films, but Se7en has the moral high ground if you ask me. It is also far more restrained - showing the gruesome aftermath and having the forensic details gorily described, but hardly any onscreen violence, give or take the aforementioned scene with Brad Pitt. Yet despite this, it comes off as far more disturbing. I needed a stiff whisky after seeing this one at the cinema.