I would go to Chef Mickeys, especially if your DD has no problem with the characters.
The pace is a little faster so you can go when you're ready to leave. At the luau, you have a whole show to sit through. There is also more variety in the food at Chef Mickey's.
My own DS is a very picky eater but we can always find something he will eat at the buffet. At the Luau, your choices are a little more limited.
It's also cheaper for you and DH to eat at Chef Mickeys. (Your DD should be free at both)
Have fun at whichever you choose!