I grew up in Israel and the American censorship rules don't apply there, I've seen a lot of R rated films as a kid and don't think it damage me in any way. I think that if you sit with the child while watching the movie and talk to him \ her and explain what's going on, reminding them every now and then that movies are about artistic expression and not representation of reality - it can be a good experience even at 12-13.
It really depend on the child and on the movie.
As far as I'm concern, I would rather expose a child to some sexual content (well, you know, not porn, but definitely some nudity) before harsh violence.