The comments on this question have most of the information that seems readily available about the differences between the movie and the film, and I myself have not read the novel, so bear that in mind.
Here's the link to the site with the best analysis I noted.
To sum up, the primary differences are:
The number of characters in the transport to Vega; in the movie, there's only room for one. In the book, it seats five.
The character of Palmer Joss is a religious writer in the movie; in the book he's a preacher.
The end of the Cold War caused one of the novel's subplots to be dropped from the film.
There are (arguably) different motivations for some of the characters in the novel than as shown in the film.
The film apparently plays the "science-vs-religion" aspect up more than the novel.
The character of Ellie didn't face the sexism she encountered in the film.
The romantic aspect of the film does not exist in the novel.
Here's another link to a Quora question with some of the same points listed.
5 people went in the book, and the conversations with the aliens were just amazing compared to movie. The conversation Ellie had with the alien alone makes the book a great read.
The endings were vastly different.
Movie: See, scientist lady! Faith CAN be good!
Book: Everything we know about the universe is wrong and the game has seriously changed. brain explodes
The movie ending had a religious bent like if millions of people can believe Ellie on faith, maybe Ellie can believe in God. Also the conspiracy aspect about the length of the static, which was suppressed.
The book ending touches the concept of reality itself, finding ordered data deep inside pi, leaving it hanging what that data may be... space bible? Encyclopedia Galactica? The Hitchhikers Guide to the Galaxy? More instructions?! I personally like to think that the data wiggles and is a nature-of-reality based universe internet. Or contains instructions to join said universe internet.