I prefer CC because that is what I own. I play BBb in Brass Band because that iis what I want to play (it makes it easier to read the treble clef parts), and I play F if the orch part calls for it.
If you have access to a better BBb than a CC, play the BBb. Of course, I say this and I DO have access to a better BBb (I have at my disposal a handmade Hirsbrunner BBb), and I still play the CC, but that's beside the point.

Play what you know. Learn what you want. Buy what you like. It's that simple. Just sound good on anything and everything that you play.
My $.14..............