We did Chef Mickey's for breakfast and have it scheduled for dinner next trip. We also have CP scheduled for LUNCH.
I would say go to CM's for breakfast and CP for Lunch or Dinner(great break right in the park. I'm sure they both do a great job at breakfast, but the Lunch/Dinner menu at CP is very special and I cannot wait to try it. I expect to enjoy Chef Mickey's dinner as well, but the fare is more standard. CP really has some tantalizing items listed.