Hey JC - haven't noticed you before. Welcome!
I am a huge fan of the CC for a lot of reasons:
#1 Fat artery clogging highs. Smooth like a baby's bottom covered in butter!
#2 Monster mids. I wouldn't say high mids - I say mid mids. High peak and medium Q if that helps...it will cut through the mix and can get nice and crunchy.
#3 Pretty good output - but not super hot. Doesn't handle/feel like a high output pup, but it drives enough. Mid boost may be a big part of that.
Some say the it has the following downsides:
#1 Not enough highs - disagree. They are there, they just are not shrieky/piercy in any way. And - a simple turn up of the pole pieces will bring them right out.
#2 Bass is flabby/loose. True. It is not a tight thumper in the booty department. However - adding shorter poles, such as from a full shred, or cutting the ones in there (careful!) will tighten up the bass.
* The amount of treble/bass is a bit of a mis-perception I think. The pup totally has enough of these. However, it has sooooo much mids the treble/bass may seem weak relative to the mids.
Remember, this is a pup originally designed for a floyd loaded strat of basswood perhaps. In that guitar, it will have a much more even response and tonally do it up right.
I like to play a lot of classic rock on mine: Clapton, Zepp, Allmans, etc...It's my go to guitar for that (Epi LP). It will also cop quite a bit of Van Halen very well too.
Definitely a love/hate pup. Very distinctive, and not for everyone. Of course, you are only a mag swap away from a regulalr Custom or a C5 if you don't dig it.