Maybe I like this Coen the most because..
it has the most fully realized human being in it. I think in a way, the Coen's always make farces. Fargo is crime-farce, Big Lebowski (which i also love) is a detective farce, Burn after Reading a spy-farce, Lady killers obviously a farce.
Even no country for old men, with all it's bleak violence and seriousness, has farcical elements in the plot, with all the running around with the money that doesn't go anywhere, the totally random car crash, the super-villain bordering on sillyness.
Now farces are great, but the thing is that the characters is farces tend to stay carictures. They're sharply drawn, 'smaller than life' kind of people. Cartoonish, fun to look at and laugh at, hard to identify with.
I think Llewyn Davis transcends this usually farcical shaping of Coen-characters. Though there are some typical farcical elements in Llewyn's 'journey that ultimately doesn't go anywhere', I could fully identify with him on a personal level. This may be the Coen's movie that moves away from farce and towards drama the most. Add the beautiful music and typically well executed cinematography, the usual Coen-brilliance in the details and the humour and I say this movie is freaking great.