Now, I've never seen the Cider House Rules...
... And Michael Caine is a brilliant actor. That's not what I'm arguing.
Perhaps it's because it was Caine's third (or fourth?) nomination, and the Academy said, "Oh, give him the freakin' Oscar already!" because he hadn't won one yet. (Hard to believe--but then, Al Pacino had about seven or eight freakin' nominations before he finally won for Scent of a Woman.)
But Haley Joel Osment's performance in The Sixth Sense is absolutely iconic. I mean, the line could've been absolutely cringeworthy, but he made "I see dead people" one of the greatest lines ever said in English-language film! In contrast, The Cider House Rules has sort of faded into the background--no one I know has seen it, so no one I know can vouch for Michael Caine's performance in it.
I love Michael Caine, but I just find it hard to believe that HJO didn't win Best Supporting Actor for The Sixth Sense.
"The life of the dead is placed in the memory of the living."
--Marcus Tullius Cicero