I would not recommend doing one without the other, because the book has some beautiful and striking contemplations, on everything from the nature of how each of us look at situations to the author's own recollections of where he got the idea from the tale. However, the strange thing about the book is that it is disjointed, and you know the ending about halfway into it. Time skips and jumps and sometimes you go to something that has already been covered, but now there is more detail. I was okay with this, but I had seen the movie first, so that might have had something to do with it.
The movie goes chronologically, making the storyline easier to comprehend, and puts in its own twists and embellishments and subtractions that I enjoyed even after reading the book. Of the two, I would have to say I liked the movie better (possibly for Juliette Binoche alone) but I would not recommend one without the other; they are a pair.