I have not seen the movie, but I imagine the pros of reading the short story are similar to other situations comparing the written work to the filmed version. When you read, you form pictures in your mind of the characters and setting. When you watch a movie, you see other people's conception of the same things. While this can be interesting, I find it also tends to disrupt the images I have already formed. If I see the movie first, I have a hard time seeing anything except the movie version in my head. For example, although Gone With the Wind is one of my favorite books, I saw the movie first; Scarlett will always be Vivien Leigh even though the first line of the book states that Scarlett was not beautiful.
For a short story like "The Lottery", another danger is that the short story is compact, vivid, and with little wasted action. I have to think the impact would be lessened when stretched to movie length.