I only just found out that The Stones used Ray Charles' version as the basis for what they did. Ray changed the words a bit from Hank Snows' original. Both included pedal steel which Brian must have picked up on for his slide guitar playing on this.
Movin On is so cool because in the best of blues/country traditions, the song reminds me of a huge train moving down the tracks and all the instruments lend to this sound to me. Then the ending sounds like this huge train has come into the station and is putting on the brakes.
I'm Alright is a great song too. I can just imagine how hard it must have been to play in time when all that screaming was going on and amps and pa's were no way able to keep up that. It's got a great ending too.