Anything covered by Johnny Cash has a different weight to it.
#Hurt Nine Inch Nails (original)
Johnny Cash (cover)
Cash's version was so great Trent Reznor even said when he saw the videoclip for the song he felt the song wasn't his anymore.
Also... Does a different singer in the same band count as cover?
If so...

Dead and Bloated

Stone Temple Pilots (Scott Weiland vocals) (original)
Stone Temple Pilots (Chester Bennington vocals) (cover)
this territory is moderated
I wouldn't call Chester's a cover but I do always think it's kind of weird when bands keep the name but have a new lead. I've always kind of avoided Chester's STP but that was really good.
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His interpretations are great. He does not try to add his own spin to songs. He was a fan of STP and wanted to give STP fans what they wanted, or something close to it.
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