I've only been to CP, will be trying LTT this trip. I can say, even as an adult, I loved CP! And we had breakfast and it was great...seven years ago. I am sure from what I have read on the boards that it is still great food.
From some others I have heard rave things about LTT which is a big reason we want to try it this trip. But, from a whole different perspective, I have heard it is a great place for food allergies, so this is the main reason we are going.
What do you think your family will like more? I think each restaurant offers something different, buffet vs family style, decor, and of course, characters not to mention food. I think, either are a fine back up for CRT.