We've done early June (once) and Thanksgiving week (many times). The crowd level in June was consistent. The crowd level Thanksgiving week varied from day to day.
We typically arrive the Saturday before Thanksgiving and fly out the Saturday after. The crowds are pleasant Saturday thru Monday or Tuesday. The crowd builds from that point on. Thanksgiving will be VERY busy. Friday will be very busy too. The crowds at the beginning of the week will be lighter than June. From the middle of the week on it's a toss up. Probably a little heavier on Thanksgiving day, especially in the MK.
We love Thanksgiving week. We do 90% of our touring Saturday thru Wednesday. We avoid the MK on Turkey Day. We tend to go to DTD on Thursday and/or Friday. If you live in a cooler climate, as we do, it is warm enough to swim. The Christmas decorations are up and you can't help getting into the Christmas spirit.