This question is often asked. In my limited personal experience when a member of both I have found:-
C&MC is more of a business, tents only allowed on a limited sites, facilities very good, but sites can look like manicured car parks. Good CL network, excellent car and van breakdown cover with MayDay for UK and Red Pennant for Europe. Excellent but VERY expensive caravan insurance. Good deals on crossings
C&CC is more of a club. Others will fill you in as we left after a couple of years.
Colin