Margaret Mitchell’s Gone with the Wind is the Southern epic. It is about the journey of a flawed heroine from a position of status, through downfall and ruin with much trial and tribulation, to a new position of some status. It exemplifies the unique traits of the Old South civilization. Southern Partisan magazine listed it as one of 15 essential books on the civilization of the American South, describing it as a "not entirely accurate...portrait of the Old South...but mostly it was," and more accurate than the movie. Two articles that treat it favorably, though having much different emphasis are:
Cantrell, James P. 2006. "The Southern Epic and Its Sequel: Margaret Mitchell and Scarlett" in How Celtic Culture Invented Southern Literature. Gretna, La.: Pelican, chapter VIII, p. 193-208.
Pattison, Robert. "Gone with the Wind: A Reappraisal," Tennessee Studies in Literature, 26, (1981), 142-156.
James Joyce's novel Ulysses is an obvious but not easy choice, The novel is challenging to read and pretty long (it took me a full week, reading 5 or so hours a day, to make it though the whole thing), but I'm certain that you would see strong parallels to the Odyssey. Those parallels aren't by chance; the modern Irish writer modeled his story pretty closely on the Greek epic, even as he changed the setting to Dublin. The good thing about Joyce's novel, too, is that it's made up of fairly independent chapters. You could read just a few chapters -- such as "The Lotus-Eaters" or "Circe" -- and use a summary to cover the gaps in your understanding of plot and characters. See the following link for an overview of the parallels:
That is an intelligent question. Comparative work is always important and can shed light on the Odyssey.
Here are a few suggestions. If you want to read the companion epic of Homer, read the Iliad. In this work you will read about the Trojan war. If you want to follow the story from a Roman point of view, read the Aenied. You will read of Aeneas who establishes a city after the fall of Troy.
If you want to read epic from a more philosophical view, then read Lucretius' On the Nature of Things. This work is about Epicurean philosophy. If you want to read epic from a comic point of view, read Ovid's Metamorphoses. Here we read about transformation and tons of mythologies.
What ties all these works together is that they are written in the traditional rhythm of epic dactylic hexameter.
Have you considered 'Gilgamesh?' That too was an epic journey - it has a hero who is triumphant, he journeyed far and wide,he is sometimes defeated or challenged or confused. He gets to face up to evil challenges and be the force of good which prevails.The story is also based on cyclical lines and older legends and myths.This epic story could also be fairly topical just at the moment for it is based around ancient Mesopotamia - the area around modern day Iraq. You could compare the different sets of hurdles the heroes have to face,and the fantasy creatures/paranormal powers.Look for the place in the tale where the hero looks as if he is finished and write how he wills himself to rise up again and go onwards.
A classic English-language epic is Paradise Lost by John Milton. While it is not an easy read, it is easily among the few most influential poems written in English in the last 500 years. It has elements which are very similar to the Odyssey (such as the story of a beleagured hero), but there are significant differences (despite being composed about two millenia apart from each other!), namely that Milton's vision was specifically Christian, while Homer's epic is about the pagan worldview. But many of the poetic conventions are the same, and a comparison between the two works would yield interesting distinctions and illuminations of each poem. Best of luck!
I just finished re-reading Margaret Walker's (nearly 500-page) novel Jubilee and think that it, too, may be read as an epic. Walker follows the life and travels of a black woman who lives through what is the probably the most tumultuous period in African American history, the transition from life in the ante-bellum South, through the Civil War, and into Reconstruction. (The Civil Rights Era probably comes in as a close second.) Much like a classical epic, this novel is clearly concerned with transforming the history of a people into a clear, single narrative and using that narrative to transmit cultural values.
Have you tried Beowulf? It has all the conventions of an epic hero. Another comparative piece that is certainly more modern is the original Star Wars. If you focus on Luke Skywalker, you will be able to make many comparison point between him and his adventures and Odysseus's. I'm not sure if you need a classical piece or not, but if so, Beowulf will work for that.
If you were to put it in simple terms the Odyssey is about someone who goes on a journey and defies the odds in order to reunite with his family. Other stories that have a similar frame would be...
The Aeneid by Virgil
The Metamorphoses by Ovid Choose your pick with this!
Percy Jackson and the Olympians By Rick Riordan (only if you want to push the envelope with this one!)
Then there is always the Iliad by Homer which is a prequel to the odyssey. You compare Odysseus's journey between then and now.
The Divine Comedy by Dante would be a good idea. The poem was written in the journey form. The poet travels from the Inferno up to Eartly Paradise. It was conceived as "the new epic of Christendom." It is a journey toward revealed knowledge, the vision of a world suffused with light:
"In that light a man becomes such
That it is impossible he should turn away
Ever to look upon any other thing."
I just read the epic of Gilgamesh in my pre-AP world history class and it is a great one to compare it to.