having played both, i prefer the custom for metal-esque riffing. tight low end thunder with lots of clarity. perfect for palm muting. think brutal crunch/distortion, tight, 'cold' with precision like a scalpel. also known as sith.
cc on the other hand, has a more overdriven quality to it. soft attack with more mids. way rounder and more musical than the custom. think warm overdriven feel, singing, less low end tightness, more fluid. aka jedi.
may the force be with you.