I've done both and, IMHO, 1900 is a "classier" place with better food. Chef Mickey's can be very hectic, and I could certainly see how a child could get overlooked. I'm sure the characters do not mean it, as I'm sure they get overwhelmed at times.
1900 seemed to be more organized. When DH and I went, we had a few characters actually sit down with us and goof around. And we don't even have any kids!
If I was planning a birthday party, I would go with 1900.