The "rock" version is released as a 7" and 12" at the time. Also available on the bootleg "Mick Jagger - The Versions".
I used to prefer the "rock" version above the album version, but listening to it now I have to say it sounds too slick and eighties to me. Even more than the album version does. But if I have to choose, I go for the album version.
By the way, Hard Woman has the worst video ever! (I guess it was hip at the time??)