But while O Brother's plot draws heavily on Homer's, the references in Inside Llewyn Davis seem to have as much to do with James Joyce as Homer. Our hero Llewyn, like Leonard Bloom in Joyce's Ulysses, has episodic hapless adventures around town—in this case, New York's Greenwich Village, with a mid-film jaunt to Chicago—with no conquering hero's end.
For all its sibling resemblance to O Brother, though, beleaguered Llewyn's real twin is Barton Fink, the unlucky playwright-turned-Hollywood-flack played by John Turturro in the 1991 film. Like Llewyn, who's living around the edges of success but manages to torpedo his chances at every turn (maybe on purpose), Barton Fink has experienced a bit of success, but is loathe to capitalize on it too much, lest he lose touch with the "common man." (Unlike Llewyn, Barton Fink is actually getting paid rather handsomely for his work.)
Both men are presumably on their way out as artists. And both are struggling with the rapid commercialization of their craft—folk music on one hand (the film covers the Village folk scene during the very last week before the Age of Dylan) and theater and film around the apex of Hollywood's Golden Age on the other. (Both also experience some trauma at the hands of a psychopathic John Goodman.)
There's some speculation that the second half of Barton Fink is all some kind of dream, and it's at least possible that most of Inside Llewyn Davis is, too—at the very least, both films let viewers dwell for a bit in their protagonists' state of mind. Ethan Coen remarked that it was "correct to say that we wanted the spectator to share in the interior life of Barton Fink as well as his point of view."
Most importantly, though, both of these stories capitalize on another of our cherished cultural myths: the plight of the creative soul. Making stuff is hard work. The roadblocks are many. (One imagines the Coens know a thing or two about that.) Barton Fink, in a film the brothers wrote after hitting a wall with Miller's Crossing, is suffering from a couple of classic artists' problems—creative block, belligerent business types, scary next-door neighbors. Llewyn Davis, on the other hand, has created most of his own problems by being a bit of a curmudgeon. But both of them are crashing and burning because they are not just living as artists, but living the legend of the artist who fights to stay "authentic."
Ironically, both men run into problems because of their idealized versions of authenticity. Barton's so consumed with his own problems that he winds up alienating the only "common man" he encounters. Llewyn scoffs openly at Jean's "careerist" and "square" and "sad" dreams of a normal life. He tells his sister he doesn't want to just "exist"—"existing ain't so bad," she retorts—and is horrified by the thought of ending up like his father, a merchant marine who's living out his days a broken-down old man in a nursing home. And he winds up loudly taunting the only truly "authentic" folk musician in the whole movie.