If the original DVD release of Joel and Ethan Coen’s “Inside Llewyn Davis” is like the bare-bones “Bob Dylan’s Greatest Hits” on CD, the new Criterion edition is like a copy of the “Biograph” boxed set. On vinyl.

The 2014 DVD release of “Davis” was just fine, but if, like me, you think the Coen Brothers’ wry and gently sad tale of an acerbic folk singer trying to make his way in 1961 Greenwich Village is one of their best films (my original review is here), the Criterion Collection edition is a cornucopia of wonders.

The film itself is either the saddest comedy the Coens have made or the funniest drama. It’s a note-perfect recreation of a time and a place, but so fully realized that it feels almost casual, the details so perfect that they never call attention to themselves. At the center is Davis (Oscar Isaac), a protagonist who is not very likable at all, his career stuck in place through a combination of bad breaks and his own arrogant self-sabotage. Given the chance to audition for a big Chicago producer, he deliberately picks the most depressing and alienating song in his repertoire, but sings it as brilliantly and beautifully as he can, making defiant eye contact for the last verse.

“Inside Llewyn Davis” follows a week in the life of Davis that’s a lot like a folk music “round,” in which various people drop in and out of the melody, singing different parts, and the song ends up right back where it started. Last verse, same as the first, a little bit louder, a little bit worse. I think the Coens find Davis’ struggle pretty funny, but they also kind of love him for his perseverance, for his inability to give up on himself. The last line of the film is Davis sarcastically shouting “Au revoir!” which of course is a French way of saying goodbye. But the literal translation is “Till we meet again.”  Next verse, same as the first.

Ported over from the original DVD release is “Inside ‘Inside Llewyn Davis,'” a fine 42-minute traditional featurette that encompasses the making of the film, featuring interviews with all the principals and behind-the-scenes footage, including some time spent in the studio with Marcus Mumford, Chris Thile, Justin Timberlack and Isaac himself recording the songs that appear in the film.

The Criterion edition adds a bunch of new extras. My favorite is “The First Hundred Feet, the Last Hundred Feet,” a wonderful 45-minute conversation between the Coens and “Crimson Peak” director Guillermo del Toro. Using “Blood Simple” and “Inside Llewyn Davis” as bookends, the conversation ranges from the evolution of the Coens’ style to the themes that run throughout their work. Joel Coen says that the circular nature of “Llewyn Davis” might be taken to be God’s punishment of Davis, a subtler variation of the tornado at the end of “A Serious Man.” Del Toro is a fan and, of course, a singular director, but he also knows his stuff, and his observations and insights into the Coens’ work trigger some interesting responses.

There’s also a fun conversation between the Coens and longtime music producer T Bone Burnett about folk music, which somehow devolves into a discussion of Burnett’s fears of a “Terminator”-like future where mercy is outlawed. (The Coens aren’t convinced.) On top of that, there’s a 101-minute concert film, “Another Day, Another Time,” featuring Isaac, The Avett Brothers, Joan Baez, Jack White and more performing their interpretations of the songs in the film live on stage.

To provide historical context, there’s a piece on the early ’60s Greenwich folk scene featuring Elijah Wald, who co-authored the autobiography of Dave Van Ronk (who the Coens pretty much admit is the model for Davis). And music writers David Hadju, Robert Christgau and Sean Wilentz provide a commentary track for the film — interesting choice, since they zero in not on the filmmaking but the historical connections in the film, who this character or that character might be based on. This might seem a little wearying — “Llewyn Davis” is, though grounded in specificity, an act of imagination — but the writers find the line where inspiration ends and invention begins.

Add a 1961 short film, “Sunday,” that chronicles a dust-up between New York folkies and the police (which gave the Coens the idea to include an autoharp player in the film) and an essay by Kent Jones, and the Criterion edition of “Inside Llewyn Davis” is a cup overflowing. I’m usually loathe to “double-dip,” but people who own the original DVD ought to embrace the film’s circular nature and buy the film again.