I have to admit - the first time I heard this song, I was confused. I knew the Velvet Underground song. Sure, some of the lyrics matched, but this was not the "Sweet Jane" I knew, from Loaded.
I was not yet aware that there was a 2nd version, which appeared on VU's 1974 live album, recorded in 1969 - predating Loaded.
And really, it doesn't matter what I think of it. This version, a cover by Canadian band Cowboy Junkies, is Lou Reed's favourite version, and since he wrote the song, I'm going with this opinion.
This version was recorded at the Church of the Holy Trinity in Toronto, straight to two-track. The acoustics in the church made for some amazing reverberation that makes this version glow.