Usually that's true. The books tend to expand much more than what can be shown in a movie. The characters are usually deeper, there's more layers to the plot, and you can listen in on what the characters are thinking about in addition to what they say. Just recently I did the opposite of you in that I watched The Hunger Games first and then started reading the books. There was so much hype for the movie that I thought that perhaps the movie could stand up on its own, but as usual I was a little disappointed. After watching the movie there were several things that the movie seemed to gloss over which I felt that the book would have done a better job. For example, the back story wasn't really talked about in the movie and didn't lead to the feeling that I felt should have gone into what the Hunger Games were all about. But after beginning to read the book I noticed how the book fleshed out some of these holes.
Every once in awhile the movie is pretty consistent with the book and can stand up on its own. I thought the most recent Lord of the Rings trilogy was good as a movie (series) without having to read the books. Likewise Harry Potter series was pretty good in the theaters and didn't need a person to read the books, or if they did read the books didn't feel like the movies were a ripoff.
Sometimes the plot in the movie and the book are so different that it is difficult to say whether one is better than the other. The rendition of Steven King's The Running Man in the movie was different than the book such that it was tough to say that the book was better. In the movie the contestant was able to go after the architects of the game show in a satisfactorily manner, whereas in the book it was a darker outcome.
And then there are the times when they make a book based off of the movie. Usually in those cases, the movie is much better than the book. I think the problem with books based off of movies is that they try to stay too true to the movie, but because the movie itself can't go into such detail that books usually are able to, the book based off the movie also feels too simplistic and flat. I thought that the movie The Game was very good but the book felt like someone trying to tell me about what the movie was about. Everything in the book was pretty much in the movie without going into detail that wasn't in the movie that may have helped make it feel more well-rounded.