In judging how great (or sad) a cover version is, we probably need to compare it against its original, since that should give us some objective measure of what the performers found or brought to their versions. So watch/listen to Tim Buckley's 1968 original version (from The Monkees television show). Try out, too, the Dire Straits original version of "Romeo & Juliet." In our view, both are dramatically transformed by the versions here.
The Indigo Girls take a great song that's a little more resigned, with an emphasis on fate (the video certainly overemphasizes this point) into a much more impassioned and personal tragic experience that might just be in a class by itself in the tournament—that is, if you're susceptible to being moved like that, as we are. It's worth noting that almost no one else of note (correct us if we're wrong, please, in the comments) has covered the song since.
It's perhaps notable that there are quite a few other cover versions of "Song to the Siren" by 2016 March Sadness teams Dead Can Dance and Sinead O'Connor, as well as Robert Plant, Bryan Ferry, The Czars, John Frusciante, George Michael, Amen Dunes, David Gray, and a whole lot more. (These are presented in roughly descending order of quality.) It's worth saying that all these versions are covering the This Mortal Coil version of the song, not the original, which means that TMC found something essential in the song and elevated it. We think that says something about just how much of a game-changer the This Mortal Coil version is. We don't believe it's been surpassed.
These are both towering songs that should have made it to the final four, but they're matched up here, and only one moves on. Personally I find this a wrenching choice, easily the hardest one to make so far, but I lean "Song to the Siren," as I think it surpasses and renders the original almost unlistenable to me. I love the Indigo Girls' version of Romeo & Juliet too, but I can still listen to the Dire Straits' song and think it good. This ought to be a bruiser.
For more information on these songs, check out our original coverage of "our original coverage of Song to the Siren" and of "Romeo & Juliet."
(6) This Mortal Coil, "Song to the Siren"
(3) Indigo Girls, "Romeo & Juliet"