My one caution about MK and rain...
If there is lightning at all (like in the spring and summer), then every outdoor ride will close for at least an hour. This doesn’t sound like a big deal if you are planning indoor attractions anyway, but it has a huge impact on all other attractions. At least on a normal rainy day, you can count on FP’s and the crazy people (guilty!) riding stuff in the rain. But when the lightning comes, every affected FP is transferred into an “any attraction, any time, except 7D” for all of those rides. And those FP’s will greatly clog up the indoor attractions.
Now, for a normal rainy day, where you are trying to stay dry, then MK or Epcot are great choices. But we usually actually prefer AK. Let’s face it, even with indoor stuff, you are going to be wet. So we just roll with it. And the animals are often more active in the rain, the Safari is awesome in the rain, and it really is a beautiful park in the rain. And Kali River Rapids is usually low crowds, and we are soaked anyway. In fact, back home when there is a nice steady all-day rain, we call it an Animal Kingdom kind of day.