While all the parks will be crowded on 12/24, the next day will be worse. MK will be wall to wall people and will probably close to new guests by mid morning. Even if you get in you will not be able to get on many rides because of the crowds. Unless you just want to say you were in MK on Christmas I'd stay away from MK.
Epcot will probably be the least crowded (or at least able to handle the crowds better than the others). Many families stay away from Epcot because they don't think their kids will like it. Also, because it is a larger, more spread out park it seems to handle large crowds better. DW and I did Epcot on 12/25/03. We got there right at opening, used FP, went to WS by lunchtime, and realized we wouldn't be able to do everything that day. It was crowded but we got a lot accomplished and had a great time.
My vote is for Epcot.