We were at both restaurants last week. We preferred the 1900 Park Fare offerings over Chef Mickeys (if we had to choose), but both were wonderful.
Honestly, the biggest difference between the two places are atmopshere and characters. 1900 PF at the Grand Floridian with Cinderella, Prince Charming and the stepsisters has a much different feel to it than Chef Mickeys with the Fab 5 at the Contemporary. We did both and were so glad we did.....they were so totally different experiences and both lots of fun!!
Contrary to another poster above, I would also recommend Crystal Palace for dinner. That one was our favourite food-wise, the restaurant was lovely (and so convenient at MK), and the characters were great.
The character meals were a highlight of our trip. Enjoy whatever you choose!!