For what its worth the movie is as close to a lteral adaptation of King's novel as any movie can be. That may be the problem. When King first wrote The Green Mile he released in a serialized fashion - six ninety page installments. As a result the flaws that can often be in even the best King books - too much attention to detail, certain characters more fully realized then others - were less apparent in a ninety page installment. Read in a collection, the book doesn't read as well as it did.
I think the movie is superb but it is at least twenty minutes too long, maybe half an hour. The Shawshank Redemption managed to deal with a life sentence and the darkness of prison in a film that is nearly an hour shorter and far better paced then the Green Mile. It's worth noting Shawshank is a novella that's less than a hundred pages and the movie never seems padded for a moment and Green Mile is five hundred pages and the threee hours in length actually feels longer even though it's covering a far shorter time period.
I think Shawshank is one of the gold standards for how to adapt a literary work of any fiction as well as one of the best adaptations of any Stephe King work. By contrast while Green Mile is a superb film, I can't in good conscience rank it among the top five film adaptations of a King Novel. (For the recrod, Shawshank, Stand By Me, De Palma's Carrie, Misery and Carpenter's The Dead Zone. Kubrick's Shining is a masterpiece but it's not an adaptation of King's book, strictly speaking.) This is a great film for every reason you say it is but I do think it's not an all time masterpiece.