This is a great question. I think the simplest way to answer the question to say that the movie, Troy, was godless. That is the chief difference. In Homer's Iliad, the gods are everywhere intervening in the lives of men. For example, in Homer's version, Aphrodite saves Paris from Menelaus. In the movie, Paris runs to his brother and his brother, Hector, kills Menelaus. One more example should suffice. Diomedes, the great Greek warrior, even at one point cuts the arm of the goddess, Aphrodite! In a word, the gods are ubiquitous in Homer's Iliad.
In the movie, the gods are absent. There are in the background at best. For example, the Trojans are portrayed as pious to Apollos, but there is no manifestation of Apollos. The reason for this fact is not surprising, because from a cinematographic point of view, it would difficult to portray the gods. In addition, there is a massive amount of material to cover and the directors have to leave certain portions out.