When Jeff Buckley covered a song it was like a doctor giving someone a heart transplant. The difference is that usually the patient was better off after the surgery. I guess the most obvious obvious example is Leonard Cohen’s Hallelujah.
Here’s an amazing version of Jeff Buckley playing Satisfied Mind, a song I was surprised to learn isn’t included in the public domain as a traditional (wiki article link). This video is from an open-mic shortly before he blew up into the almost mythical figure he soon became.
Here’s the first version I heard from Sketches for My Sweetheart the Drunk, an album of personal demos and rough recordings released after his untimely death in 1998.