Chef Mickey's is an event in and of itself. The photo opps, the great interactions with the characters, the number of characters - they are the tops at WDW for this on a consistent basis. We've done both breakfast and dinner numerous times since my kids were preschoolers, and now that they are 12-22, this is still one of the restaurants that they insist on going to every time we visit WDW. The food is actually pretty decent. The last time we went, we were a party of nine, from three generations, and everyone found something to like at the buffet.
Cape May Cafe is busier at dinner, when it's seafood and no characters. I'm not a seafood person but I still enjoy dinner there. If you are planning on going to the breakfast with the characters, it's pretty quiet. There are only three or four characters, all dressed in beach gear. I found that they were nice and friendly and posed for photos, but this is not the high energy hugging and napkin waving and dancing characters from Chef Mickey's. The breakfast food is pretty much the same, so if you are considering breakfast at both places, you might want to consider the temperament of your children and their reaction to the characters. CMC might be better for a first time, or kids who might be overwhelmed by the noise and energy of CM.
If you do both, I'd recommend breakfast at CMC and dinner at CM. For another good alternative, the breakfast at Ohana is family style, so they bring the food to you on an unlimited basis, and the characters are a little different - you will see Lilo, Stitch, and Pluto there, plus maybe Minnie and Mickey, and it's also a little slower for more interaction time with the characters.