Okay, this one's freaking me out, mostly because I had no idea.
Remember Millie Small's 1964 Brit Invasion hit "My Boy Lollipop"? The record that, in retrospect, turned out to be the first exposure any of us State-side had to the pre-reggae Jamaican music called ska? And, coincidentally, the song that put Island Records honcho Chris Blackwell on the map?
Well, turns out it's a cover of an obscure 1956 r&b hit by Barbie Gaye (no relation to Marvin)
I think in this case the cover is clearly better -- it's better sung and much poppier (the horns are an added hook) and, well, just better.
Incidentally, if you're wondering why the hole in the Barbie Gaye label is so small, that's because it's a 78 rpm record. Back in 1956, you could still buy pop singles in two formats, i.e. either easily breakable ten-inch 78 or the more familiar seven-inch 45.