I read the book first whenever possible and see the movie second. Without exception, I find the book version much better. A good author takes us into the characters' thoughts and feelings that they don't always voice out loud, which gives us deeper insight into why they do what they do throughout the story. This is much harder to portray in a film, so the filmmakers usually either cut it out or try to work around it. It usually comes across as forced and shallow--example: the Twilight films in my opinion.
Filmmakers have to do what they have to do when it comes to showing what's going on in the characters' heads, but viewers who have not read the book first sometimes miss things. Another case in point: I read The Hunger Games weeks before seeing the film with my fiancee. She hadn't read the book and had no idea what the three-finger funeral salute meant at the reaping early in the story. It was part of the book, and the filmmakers left that background info out.
My overall answer: read the book first; it's a deeper and richer experience almost without exception.