Any time there is a movie/book combo that I even THINK I want to read the book, I choose to read the book first. Otherwise, when you try to read the book, you have someone else's "vision" of what everyone looks like and the scenery and clothes and EVERYTHING all mixed up in your head. And you can't make your own vision in your mind's eye. Drives me crazy to be reading a novel and some actor face keeps popping into my head, instead of letting the author's words craft a visual image for me.
The ONLY time I have ever done the opposite (saw the movie first) was with Lord of the Rings. And I was glad I did. I read The Hobbit as a tween, and I remembered there being SOOOOO many various "characters" (creatures) that I had a hard time keeping them straight. The Lord of the Rings was like that also, and actually seeing on the big screen that "Aragorn" was a man, and "Gimly" was a dwarf, and Galadrial (?) was a forest queen/elf (or whatever she was), and "Legolas" was an elf, "Treebeard" was an Ent, and on and on and on.... That made reading all the names much easier.
In a way, the name thing was reminiscent to me of Dostoyvski's "Crime and Punishment", as I had a terrible time keeping the characters straight reading that, because the names were so foreign.
Other than that, I would always (if I know in advance that I want to read the book) choose to read the book first.
I did not plan to read "True Grit", and thought the recently made one so outstanding, that I bought the book and read it after, though. So did both my kids (read the book after, b/c they liked the movie so much).