Heh, that's funny. I read The Fault In Our Stars, and I wasn't sure how the book could be translated into a film, but apparently you enjoyed the film as much as I enjoyed the book.
When I don't have much time, I don't read or watch anything. Is that a better choice? Probably not.
I would read the book, if only because you're inevitably going to forget the film after a few months. Reading the book will help the story stick in your mind. I mean, if you want a story like that to stick in your mind, anyway. Besides, there's definitely some stuff that they wouldn't have been able to put into cinematic format.