I actually had a pretty different reaction to Se7en and Silence of the Lambs. They both disturbed and scared me (I saw each only once), but for Silence, I was able to keep more of the mental distance I need in order to be able to enjoy horror.
It's not the gore in Se7en (or Silence, or the chest-bursting scene) that got to me, by the way. It's rather the entire atmosphere. Both Alien and Silence of the Lambs present a world that has both good and bad aspects to it. It's a world where horrible things happen, sometimes to good people, but with enough resourcefulness and luck you may fight back. Some people will win the fight, and some people will lose, but life, in both these worlds, is worth fighting for.
In Se7en, there was exactly one good thing in the movie - Gwynneth Paltrow's character and her relationship with her husband. Everything else is grimy, disgusting, and evil. And the good in the movie is killed off off-screen, while everyone's attention is elsewhere. That's what really got to me about this movie. The horrific acts performed are really just a distraction; there's no real point to stopping a killer since life in this world isn't worth living anyway. Maybe for some people that makes it a better horror film, but for me it makes it something I just don't wish to engage with.