The first thing to keep in mind is that the two epics are written from two opposing points of view: the victorious Greeks (for Homer) and the defeated Trojans (Virgil) who are destined to become the Romans. One thing the two poems have in common is the epoch making nature of the war; in both epics, the various battles and heroes are known by everyone from the Sirens to Dido in Carthage.
The various stories in The Odyssey involve the heroes trying to return to Greece. Some, like Nestor, are favored with a swift passage home. Some, like Ajax, are destroyed due their hubris. And others, like Menelaus and Odysseus, have long, purgative journeys that take years to complete.
The Aeneid is different. Aeneas and his crew are among the few survivors of the destroyed Troy. He is given a mission to rebuild a new city in the west, but what he finds out later is that the new city is not to be a new Troy. Rather, Aeneas has to give up the idea of being a Trojan and get on with the business of establishing something new--the Roman Empire. So, although Aeneas and Odysseus both sail west and although they encounter some of the same adventures (such as the Cyclops or going to the underworld), the purpose is different.
Much more could be said about this interesting topic, but I hope this, along with a review of the plots of the two epics, is a start for you.