I also don't see the reasoning behind signing DK over CK, and I'm going to assume the Braves can only afford one of them.
Like Bumgarner, DK would be an improvement in the rotation, but it seems like CK would be a bigger improvement in the BP. CK should also be ready to contribute a lot sooner than DK.
Perhaps the issue is that DK is willing to take a reasonable 4 month deal, while CK is still holding out for 2.5 years. If that's the case, I'm glad the Braves are going nowhere near that type of contract for CK.