This is a good question and we can say that there were many differences. Let me list a few of them for you.
- Achilles was dead by time of the Greek made the Trojan horse to take over the city.
- Thetis, Achilles mother was a sea-goddess. The movie does not really make this point.
- The armor that Achilles wore and the other soldier was anachronistic.
- Patrocolus was not Achilles' nephew as the movies states. The relationship between the two men is not completely clear in the book.
- Achilles is much more godlike in Homer's book than in the movie.
With these points made, it should also be pointed that the movie does a pretty good job in showing the rage and insolence of Achilles and his hatred for Agamemnon.