We have done both and 1900 Park Faire is something we now do every trip - Chef Mickey's only once.
The interaction at 1900 Park Faire is great - Mad Hatter is hilarious and the other characters are lots of fun. We never feel rushed there and the buffet is definitely the best on property for breakfast. Chef Mickey's we felt rushed and the food wasn't any different than any where else. 1900 Park Faire has the fabulous omlette station as well as all the other goodies.
The neat thing about 1900 Park Faire is that you see unusual characters - Mad Hatter, Alice, Mary Poppins - that you don't see everywhere else. I love Mickey but you can see him in the parks also.