Category 1: Gravitas: Probably the one thing that makes the Mona Lisa so compelling is the "enigmatic smile," that slight upturning of the corner of the lip that makes her expression so mysterious. Also, she was painted by perhaps the most famous artist ever to live. On the other hand, since she is a painting, the Mona Lisa has very little to offer conversationally. Still, while Kardashian is technically capable of speech, everything that comes out of her mouth has actually been scientifically proven to make everyone who hears it dumber. We're giving this one to the Mona Lisa.
Category 2: Attractiveness Let's get this out of the way: If there's one thing Kim Kardashian has going for her, it's that she's a smokin' babe. Really, that's pretty much the only thing she has going for her. But it is something. The Mona Lisa, on the other hand, mysteriously lacks eyebrows. Maybe they didn't have them in the 1500s. Maybe she was going for a Syd Barrett kind of thing. Either way, the score comes out tied: 1/1.
Category 3: Hilarity with mustache Marcel Duchamp only added to the genius of the Mona Lisa in 1919 when he drew a mustache on a cheap reproduction and named it "L.H.O.O.Q." (if you pronounce it in French, it sounds like the equivalent of "She has a hot ass"), thus subtly and adroitly commenting on appropriation and the boundaries of art, and being hilarious in the process. The mustache on Kim Kardashian was drawn by us. And honestly, we didn't even do it ourselves -- we gave it to our "mustache-drawing" intern. And even though it is pretty funny, and Kardashian with a mustache looks weirdly like Robert Downey, Jr., in Iron Man, we're going to hand it to the Mona Lisa -- even reduced to a dirty joke, she has culture, whereas Kardashian is basically the cultural equivalent of a dirty joke.
So Kim Kardashian loses. And so does France.