Gender bender

The Sundays - Wild Horses

Aretha’s cover of “Respect” (Otis Redding)

Joan Osborne's version of Slim Harpo's "Shake Your Hips." Smokin' hot! Her version of "What Becomes Of The Broken Hearted" is also fantastic, though maybe not "better" than the original by Jimmy Ruffin.

From the opposite end, in 1956 Elvis leveraged his popularity to sell 10 million copies of "Hound Dog" which was originally performed by Big Mama Thornton in 1952.  Big Mama's version was infinitely better and helped shape rock and roll for guys like Elvis who profited to an incredible degree from her work on this particular cut.

Not sure about better, because I love both versions - Rickie Lee Jones, Show Biz Kids (Steely Dan)