I think as a general rule we can expect not to enjoy a movie based on a book we really adore. Two personal examples are Sphere, the movie of which I was seriously disappointed in, and The Princess Bride, which I felt came up short. With subsequent viewings these movies seem much better to me than the first time.
I have not read The Green Mile yet, and can't comment, other than to say what I've already said, except I know that The Green Mile movie is a very good movie. I think subsequent viewings of it only get better.