I'll chime in as we've gone this week for the last couple of years.....
Thanksgiving week:
Sunday, Monday, Tuesday - Very light and manageable crowds. MK is typically pretty busy on Sunday as it is an EE day.
Wednesday - Somewhat larger crowds, but manageable.
Thanksgiving - Crazy huge crowds
Friday - Crazy huge crowds
Saturday - Crazy huge crowds
Sunday - Marginally large crowds early, but tapers off pretty nicely later in the day.
As an example: I arrived at MGM on Thanksgiving day 2001 at official opening to buy my limited edition annual passholder pins. By the time I bought the pins (At the big sorcerer's hat) and made my way back towards the entrance, the posted wait for RnRC was 100 minutes and ToT was 80 minutes.
Now, I did not actually walk down to the attractions to verify, but there were SO MANY more people on the street than any other day we had arrived at park opening. It was like a night and day difference.
We've altered our trip plans this year to arrive the Thursday before Thanksgiving and go home on Thanksgiving day. The crowds on Thursday, Friday and Saturday are just more than we care to deal with. We'll use Wednesday as our Downtown Disney / outlet mall shopping day before heading home on Thursday.
I don't want that to scare anyone because Disney can be lots of fun at any time of the year if you want it to be, but the crowds will be significantly larger on Thursday, Friday and Saturday. There is no way you couldn't tell the amazing difference if you are there both parts of the week.
Hope this helps!