I used Dr. Kirk's Scratch Freee for the first time a couple of days ago. Dr. Kirk's is a fairly thick paste wax mixed with EEE buffing compound. I think this is essentially the same as EEE UltraShine, jut a bit less expensive here probably because its made in USA rather than Oz.
Wood was mesquite, piece was a bud vase, finished in a DIY version of shellawax (carnauba paste wax mixed with a little shellac). I sanded to 800 grit, applied the Dr. Kirk's with the piece stationary, and then buffed it on the lathe using paper towel. Then applied the shellac/wax.
Obviously, this is a limited test, but I can compare it with a cocobolo vase that was done with only sanding and the shellac/wax - the vase with the buffing wax is clearly a bit shinier.
So bottom line - I'm happy with the results that I got.