One of the fascinating things about these ancient stories is to see how they reflect the current culture of wherever and whenever they are recounted. For example, Alexander the Great has been recounted as a Greek hero, a Macedonian hero, or even a Muslim hero. Stories have always been malleable. Scribes would make small (and sometimes large) adjustments to stories, which over time could lead to entirely different plots. People recount stories from memory, and often make up details they can't recall.

I personally believe that stories like the Iliad and the Odyssey were more like a performance art. Someone would tell a story, while the audience would come with suggestions "he killed the Cyclops!" "the wine was poisonous!" "they hid among the sheep!", and they would change the story according to the mood of the room. Similar to how DnD works today. If this is true, there can't even be a definitive true original story. This opens up many cans of worms like "who decides the cannon? The author or the audience?".

Nolan's movie is in many ways a good adaptation (it's fun and engaging to modern viewers), while also being a great reflection of current Hollywood (casting, substitution of religious plot for natural plot).