They are both equally bright to me. It just depends on how many ids you want.
Brighter (more trebly) than a JB?.
Either one can take an A2 magnet for additional high softening, yes?
plenty of people rock a cc in the bridge of a les paul and love it
Just saw a comparison video between the JB and the CC. The CC has highs indeed, just a bit sweeter than the JB's. Both sond very nice.
May I ask why you can't use the Tone knob? Or perhaps go to 250k pots if that's an issue?