The cdp is a package that is available on most Kimber models. It stands for custom defense package. I am not sure how much internal changes that the package gives but there is a melt down (rounding of the edges), some added checkering on the front of the grip, and I believe night sights.
The basic compact is about $300.00 less than the compact CDP.
I went with the compact because of carry and that reading on the forms that out of any barrel shorter than 4" your round loses effectiveness and that the gun might not be as reliable as larger pistols. This being caused by the shorter cycle time of the small pistol. I have heard good things about the Ultra model though.
The compact has the shorter grip than the full size and a 4" barrel instead of the 5". I have the alloy frame on my compact and the recoil is very mild.