I read the short story about a year ago. It is a quick read, but was powerful. I was emotionally very struck, but (like in the movie) the heart of the emotional hit comes in the closing sequences -- the postcard being returned, the phone call, the parents' ranch, the end. It took me awhile to recover, and that (frankly) was the one thing that lingered most about the story.
I went to see the movie a week ago and was even more moved by seeing the visual representation. I love to read, but visual cues are very powerful for me. (I read an interview with Annie where she says she had finally managed to put Ennis and Jack to rest about 6 months after publishing the story in The New Yorker. When they screened the movie for her, she said it all came rushing back and they were immediately back in her head in a powerful way.) I have spent the past 9 days reeling a little and trying to understand my personal connection to the movie.
Last night, in preparation for a second viewing of the movie tonight, I re-read the story. I was surprised by some of my reactions. It was not as emotionally moving this time. In the end, the story is a very direct telling of the most basic plot points from the movie. The two storytelling mechanisms are very true to each other. But (largely by requirement) the movie extrapolates a lot of the story. The Cassie scenes are a line in the story. Most of Jack's family life is drawn from small mentions in the story. Jack driving to Wyoming after the divorce is sort of a one-line afterthought in the book. The end of the story was still powerful, of course. But I felt sort of like "okay, this is not quite how I reacted the first time."
I also had a very different reaction to the characters. Ennis is more open and human in the story. As people have pointed out elsewhere, he is more verbal in connecting with Jack. When they are in the motel upon their reunion he tells him how much he missed Jack over the four years. That he had sort of given up on ever seeing him again. And most importantly, that he had taken a year to figure out that he "never should have let you out of my sight." That may not have rang so true in the movie, but would have been a beautiful line of dialogue to include in the movie to help show how Ennis really did feel connected to Jack.
Jack was also less appealing to me in the story. In the movie, Jake nails exactly how I want to think about Jack. The subtle ways he tries to pry the lid off Ennis' resolve about being together. The softer and more loveable ways he displays his emotions. In the story, he is a bit more detached actually. He has missed Ennis, but that has not kept him from sowing his oats all over. He seems less a romantic character, and I got less a sense of his yearning for Ennis.
So, I love both, but will always find the movie version more in line with what I want the story to be.