The character of Isaac is probably cut the most and he is a little more light hearted in the movie than he is in the book.
The biggest, and most important, of the similarities is the authenticity of the dialogue the characters use in the movie and the book. One example of this is Hazel and Augustus decide that “okay” would mean “always” for them and this meaning is kept in the movie version. Another important carry over from the book is how Augustus uses a cigarette as a metaphor. He will put the cigarette in his mouth but never light it because they can’t kill you unless you smoke them. Since he does not actually smoke them he has control over the cigarettes power to kill unlike the cancer which he cannot control.
The movie is a faithful adaption of the novel. Like any adaption it is a subtraction process as scenes are removed in an effort to make a compact narrative. While there are certainly differences between the two adaptions the most important parts of the story are in the film and it captures the initial emotion felt from the book. It’s clear that what was left out of the movie adaption was clearing thought out so to remain true to the author’s original