I reckon The Screaming Jets version of Eve of Destruction runs rings around Barry McGuire's original, as too their version of Shivers, as opposed to the Nick Cave's Boys Next Door version.
A few more come to mind, which some folks might consider blasphemous, but no worse than preferring Madonna's version of American Pie to Don McLean's...
G'NR's 'Sympathy For The Devil' vs The 'Stones (possibly blasphemous??).
G'NR's 'Knockin' On Heaven's Door' vs Bob Dylan (possibly again??

)
Pearl Jam 'Last Kiss' vs J Frank Wilson & The Cavaliers.
Green Day 'I Fought The Law' vs Bobby Fuller 5 (& The Clash & The Dukes from the
Reckless Kelly movie).
Jimi Hendrix 'All Along The Watchtower' vs Bob Dylan.
Jeff Healey Band 'While My Guitar Gently Weeps' vs The Beatles.
Metallica 'Whiskey In The Jar' vs The Dubliners (& Thin Lizzy & no end of Irish folk singers..

)
Metallica 'Turn The Page' vs Bob Seger.
Plenty more I can't think of right now......