We've been to WDW for the week of Thanksgiving for the past eight years. If we get a crazy hair and dare to venture into a park on actual Thanksgiving, it has been . . . Epcot. Yes, ALL the parks are going to be busy. But, it seems to handle the crowds the best. One year, we decided to visit MK for EEMH on Thanksgiving and had an amazing time once the crowds left.
Another year, we went to the MK on Christmas Eve. It was busy, but manageable. We had a great day! Since then, I've actually stopped reading all the hoopla about avoiding MK and Epcot on holidays.
(Those are usually the same people who recommend that you don't do Extra Magic Hours.)
My personal recommendations:
#1 Epcot
#2 MK
#3 DHS
and as a "last resort"
#4 DAK
(BTW - We love DAK, just not during the holidays!)
Have a magical trip!