What people are going to miss if they only see the movie (although the movie certainly does follow the storyline of the novel very closely) is one of the best use of unusual literary conventions I've seen. The book is written in first person by the title character, and as the title character's writing improves, the book becomes more complex and also more easy to read.
The beginning part of Push/Precious is very difficult to read both because of the extremely difficult subject matter and because Precious can barely write. But as she works with her teacher Miss Rain (who figures even more prominently in the book) she is able to write more clearly and put together sentences in a way that the average reader will understand. As Precious' writing improves, so does her ability to communicate her world. To be, that's one of the strongest points of the book, and why everyone who sees the movie should definitely follow up with a trip to the library to get the original book.