First, you may want to familiarize yourself with our earlier coverage of "Hurt" and of "Fake Plastic Trees."
Unlike a lot of the pairings in this bracket, these two songs are contemporaries. In fact, they're old rivals. The albums they appeared on were released a year and five days apart; the singles were released less than a month apart in April and May 1995: it was a great month for sad, bleak songs.
Well, how to compare these two sadnesses? "Hurt" is obviously working on the wounded-withdrawal axis of sadness, articulating a purely and intensely self-destructive personal malaise (in the direction of Swans, Elliott Smith, Replacements, and Joy Division). It's the darker, sonically, of the two, with the goth leanings, and it's apparently the angrier, too, so if that's if how you want your hurt, then this is your jam. It's also the more varied of the two, sonically, in terms of how it builds toward that loud distorted moment at around 4:40. Its ugliness is sonic, angry, and explosive, but the thing we've always admired about Reznor is how even among the industrial sonics, he's always had an excellent ear for the melodic. (In fact, he sings backup on "Past the Mission," a song from Tori Amos's second album Under the Pink, and if both Amos and NIN advance they could meet in the elite eight, which would be a lovely pairing to consider.)
The melodic is where we begin "Fake Plastic Trees," and the song never lets go of it. Identifiable from the first chord, it's a slow burn to a brilliant climax, even if it's a little less dramatic than "Hurt." It never loses control in the way that "Hurt" does (or seems to, rather). It's much more clearly a disconnected lament than Nine Inch Nails' entry, and it becomes unexpectedly personal at the end.
Both are big, sweeping dramatic songs. To my ears, "Fake Plastic Trees" has more of the feeling of a generational anthem than "Hurt" does, and that's why it's got a 2 seed, though that impression may be a function of the video's shots at consumer emptiness. That critique's a little clunky by modern standards, though no less relevant. Hard to pick your poison here: do you want your sad sensitive and withdrawn or really sensitive and withdrawing? Odds favor Radiohead, especially given their strong showing in the first round, but this is anyone's game.
(7) Nine Inch Nails, "Hurt" (oddly for the time and the cultural saturation of the song, there was never an official video)
(2) Radiohead, "Fake Plastic Trees" (official video)