Those who have both seen the movie and read the book say that the two are quite different. There are some themes and ideas taken from the novel and many of the same character names are used, but the story is very different and even the characters themselves are different individuals. The book is set up as a mysterious frame narrative in a contemporary setting from the point of view of descendants of each of the magicians, and we learn about the rivalry through diary entries read by the descendants as well as their personal experiences and discoveries.
Major plot points were completely changed: Julia does not die; Sarah does not die; Borden is not hanged. (He is not even convicted, tried, or accused of killing Angier); Borden and Angier are not colleagues, they barely know each other; Borden does not kill Angier; Cutter is only a minor character. Cutter convinces Angier relatively early in the novel that the Bordens are identical twins. Later, Angier investigates the birth records and discovers that there is no record of a twin. (Albert has a brother, Freddy, who is 2 years younger, but a photo shows that they look nothing alike, having different builds and facial features. In the novel, this is revealed to have been doctored, and that they had planned their trick from an early age.)
Another major change deals with the Tesla machine. In the novel, the machine is clearly shown to be a teleportation device, but does not create living duplicates. The item or person in the machine is teleported to a new location and inert material that looks like the original is left behind (in the novel, Angier refers to these as "the prestige materials"). The prestige materials do not decompose over time, even after a century, but remain exactly as the were at the moment of duplication. The only time two living duplicates are created in the novel is when an incomplete transfer occurs after Borden turns the machine off in mid-teleport. Most of Angier stays behind, but a small mass (he is viewed as a ghostly image) is teleported. There are two distinct minds (with similar memories) with very different bodies. The teleportation device becomes Angier's way to immorally improve his position in society, because, against Tesla's warnings, he uses it almost entirely to create duplicate gold coins, and sometimes paper money amassing a fortune for his family.
At the end of the novel, Angier is in fact still alive, in this ghostly form, even a century after the novel's main Victorian events. The novel even suggests that there is some psychic link between the teleported body and the prestige, suggesting that they think and feel the same to some extent. It makes the ending of the novel more haunting as we imagine he may have lost a part of his "soul" with each teleportation.
The end of the novel in fact verifies that the prestige material (the duplicate body) while rigid and immobile, possess a soul. Only one person other than Angier is transported, and this is a child we learn is speaking telepathically with the main narrator of the novel, the grandson of Borden. The "ghost" version of Angier asks him, are you leaving, or staying here with him. Obviously suggests that he is aware that these prestige materials have souls.