I recommend Chef Mickey's!
I attended Chef Mickey's Character Breakfast last August. At the time, I was in my late 30's, and I absolutely loved it. It has a very Disney feel to me.
I did not do the Cape May Character Breakfast, but I did have dinner at Cape May Cafe in August. It was nice, but it didn't have the same classic Disney ambience to me. It still felt like Disney, but it was more like Disney on a New England seashore. Whereas, Chef Mickey's was totally classic Disney. (Think Mickey Mouse Club.)
The food was good both places, but a little better at Chef Mickey's.