I can't comment on Thanksgiving, but we just got back from a trip from Dec 25-31. It started out crowded but manageable for us, but the crowds steadily grew throughout the week. MK was closed around 11:00 on 12/29, AK was closed sometime in the morning on 12/30, and I think MK might have been too. Wait times for many rides were 1 1/2 to 2 hours long. The only ride we rode on our last day was Mission Space, because we were at Epcot 20 minutes before it opened, and we still had a 25 minute wait once we got to the ride! We ended up spending more time having fun in the stores and people watching(and eating!).
I have been wanting to see WDW at Christmas for some time, so I am glad that we went, but I doubt we will do it again during that week. We had all our ps times in place before we went, but we saw many people turned away that did not plan ahead. On the night of 12/28, we watched group after group try to get seated at Crystal Palace as a walk-in, only to be told that all sit-down restaurants were filled for the night, and the CM was recommending room service instead.
Don't get me wrong, we still had a good time! We saw Cirque Du Soleil, the Candlelight Processional with Gary Sinise, DH did the Richard Petty Driving Experience, and other non-park activities. We did have fun in the parks, too, we just didn't do that many rides. I think if we want to see WDW at Christmas time again, we would go for a long weekend earlier in December or maybe even try it at Thanksgiving. Hopefully you will hear from people who went duirng that time to give you a comparison of the crowds.