I have the CGW race hammer that I run on my primary carry gun (CZ P01 w/ pro package) it runs great and is super easy to cock (something really only relevant for dry fire in my case). On my back up carry gun, a standard P01 steel frame with the factory ring hammer, I find the ring hammer more comfortable for carry, just because when I am bending over or walking a lot it is less irritating. Obviously this will depend a lot on your body type, carry position, holster, and whether you carry cocked-and-locked or decocked. All in all, I would probably go with the ring hammer if it will be a carry gun just for that slight difference based on my carry set up.
If there are any differences in the trigger pull between the two CGW versions, I am not sure, I would imagine it is just the spur that is contoured differently but that would be a good question for CGW.