They serve different purposes most of the time, so a straight comparison is not possible.
PC is normally used against the control to assist your beatdown win condition, i.e. winning by damage.
CC is normally used against the beatdown to slow down your opponent enough that you can win by either damage or deckout.
One deck will always be the slower one and thus becomes the control deck. If it can't control, it's a bad deck (good ol' slow rushes) or a terrible draw.
Outlier situations do exist where PC can slow down the beatdown's offence significantly if they're doing a lot of damage with Arsenic, Fahrenheit or Catapult. All of these options are competitively viable, which is one of the reasons a control deck almost always wants PC. The other is, of course, when the control turns into the beatdown in the case of control vs. stall.