Movie: Main protagonist's name is Cage
Book: Main protagonist's name is Keiji
Movie: Mimics are comprised of the Omega and the Alphas
Book: Mimics are comprised of the Nexus and Antennae
Movie: Killing an Alpha causes the time loop to reset
Book : Killing either the Nexus or the Antennae can cause the time loop to reset
Movie: Only Cage is a looper, Rita used to be a looper
Book: Both Keiji and Rita are loopers
Movie: Getting to the Omega and killing it will end the time loop and stop the alien race
Book: The Nexus needs to be killed only after all the Antennae have all been killed
Movie: The ending of the Movie, Cage kills the Omega, and is reset back to an earlier time, the entire alien race is dead, no one knows that Cage did it, the world goes back to how it was a day prior, Rita is alive, happy ending.
Book: In the final time loop, once they have eliminated all the Antennae, Rita attacks Kaji telling him that they have been in the loop so long that they have become like the Antennae, unless one of them dies, killing the Nexus will only cause the loop to reset. Keiji kills Rita and is crowned the Hero Of The War.
Here's a link that describes the movie plot and it's apparent plot-holes in more depth:
Edge Of Tomorrow Explained