I love The Shining, as I'm a huge Stephen King fan. Kubrick took some strange liberties with the film and left some rather important plot details out, but nonetheless it was a good horror film.
As for the best of the two, my vote goes with The Exorcist. It's much closer to the book, for one thing. I'm not sure it's a better filmed movie than The Shining, but I'll say this: The Shining gave me the willies; The Exorcist scared the ever living shit out of me when I was younger. On some level it still does. The idea that someone's innocence, freedom, and will can be removed of them by some unseen, preternatural force is disturbing and, I think, something everyone fears.