Advantages of CCPM: Fewer parts, less complicated to assemble and repair, distibutes the forces over several servos.
Disadvantages of CCPM: Almost demands very precise servos, very sensetive to proper setup or you end up with interaction between functions (even with proper setup you can have a small amount of interaction).

Advantage of mechanical mixing: Less confusing radio programming, no interaction between controls
Disadvantage of MM: More parts, not much else - mechanical mixing works just fine

Ben