Listened to it. Wasn't the biggest fan but I am also a pretty big Demon fan. Thanks for bringing it to my attention.
To contribute to this thread I'll say that Judy Garland's Zing Went the Strings rendition is the definitive version of that song. Lemmy's pre-Motörhead band The Rockin Vicars also has a GREAT cover of it too.
Jeff Buckley's covers are usually better than the original:
Lilac Wine (debatable)
We All Fall In Love Sometimes
A Satisfied Mind
I Shall Be Released
Just Like a Woman (debatable, but I think he gets it by just a smidge)
Chinese Democracy-era Guns N' Roses did an absolutely impeccable version of "Sailing."
I think these have all already been mentioned, but:
Johnny Cash - Personal Jesus
Johnny Cash - God's Gonna Cut You Down
Fiona Apple - Pure Imagination
Janis Joplin - Me and Bobby McGee
Chris Cornell - Billie Jean
Black Rebel Motorcycle Club - Chelsea Hotel #2
Aerosmith - Love Me Two Times
Disturbed - The Sound of Silence
Dio/Yngwie Malmsteen - Dream On
Amy Winehouse - Valerie
Rage Against the Machine - Maggie's Farm
Guns N' Roses - Jumpin' Jack Flash
Rainbow - Mistreated
Pantera - Planet Caravan
The Animals - The House of the Rising Sun
Judas Priest - Diamonds and Rust
Judas Priest - The Green Manalishi
Gary Jules - Mad World
I don't think it's better per se, but I do think Yngwie's cover of Gates of Babylon is pretty fucking close.