Jack,
Depending on your goals, I'd recommend removing both. For the reasons already mentioned, removing the large CCs should create more biomass for other species and release some of your larger forage from predation (Do you have BG/RES/CNBG, etc.?). Since you said you have quite a few of the big ones, I think it would be wise to at least take some of them out, unless large CC are your management goal.
How many 12-13" bass do you catch? Do you catch very many that are either smaller or larger? To release some of your smaller forage from predation and to allow the remaining bass to grow, removing some of the 12-13"ers could be beneficial as well.
Removing both would allow your forage to rebound slightly, which would in turn help all remaining predator fish. I've noticed a cycle in the effects of harvesting. I've been trying to do exactly what I advised here and have noticed the upswing in BG and RES populations in that pond. But now, the bass and remaining CCs are growing, and the BG and RES populations are taking a hit again. Eventually it will be time for more harvesting. It's an interesting dynamic.
