Sometimes, a song just sounds like it was meant for a group to perform. Sometimes, it sounds like they wrote it for themselves. This is one of those songs. When I first heard the song, I thought it was theirs. It certainly sounds like the kind of stuff that Jack White writes.
And when I heard the Tegan and Sara version, I thought THAT was the cover. It wasn't.
I was wrong, but that doesn't diminish the great song that Jack and Meg White crafted. It just means that someone else did it first. The two versions of the song go at approximately the same pace, but the hard edge of this version strikes a sharp contrast with the folky sounds of the original. Jack White can only harmonize with himself here, but it works, as well as the original, in a different way.