I expect it wholly depends. I see children--as in well before their teens in many cases--taken to R-rated movies all the time. At the video store, I see children take up slasher flicks that I won't watch myself, including the "torture porn" stuff. Once, I heard a mother say, "No, put that back...we've already seen that 5 times." And if they can handle that stuff, surely they can handle BtT.
Other children have a problem with movies like Monster House or Nightmare Before Christmas. I myself had nightmares after seeing Return to Oz, and whenever anyone says anything about me getting a dog, I STILL think of Old Yeller that an elementary school inflicted on me like 3 years in a row. For that matter, I remember crying when watching The Lion King at the cinema when I was 11, IIRC. To this day, I don't take it for granted than any Disney flick is gonna be without someone major dying dramatically. :p
Oddly, I saw the old Salem's Lot roughly around the same time I saw Return to Oz (I was about 9), and I found Salem's Lot boring (and fell asleep through part of it) and RtO frightening. I saw them both again as an adult and found RtO on the cute side and the old Salem's Lot on the scary side. I don't know why, I guess I understand the context Salem's Lot better now and RtO was a bit hard to take as seriously as when I was 9, but that's just a guess. (RtO was more depressing to me as an adult which I also think is because I understood the context a lot better--as a child I considered it happy since Dorothy lives to escape all the bad people.
)
As for me, I loved a lot about BtT, and I think I'd have liked it a lot as a child--not sure how I'd have handled the ending, and it might've taken it awhile for it to sink in (so I might have a delayed reaction, or react much worse upon watching it again).
What I don't like the deceitful trailer (which I think was made to "piggyback" on the success of some of the other fantasy movies that were popular). Interesting enough, the Japanese trailer was honest to the point of spoiling it, IMO--though NO ONE could say they'd been "tricked" into seeing it after seeing that one.