Having never heard the original - no surprise given that I'd never heard "Metamorphosis" or, from the track-listing, anything from it - I made the customary visit to YouTube:
Again, I prefer the cover. It's not that I'm anti-Stones, it's just that this song suits being a chirpy girl group number more than a languid, slightly off, pop-psych number. There's something of Petula Clark backed by The Move to The Parting Gifts version - a fine concept in my book!
* From their 2010 Norton Records split with The Great Gaylord and The Condo Fucks