We were there this past Thanksgiving week and the week after.
Sat/Sun/Mon/Tue/Wed were actually pretty good; we stayed out of the parks on Thanksgiving day, Friday (which may have been a mistake on our part because several CM's told us the parks weren't that bad on Friday) and Saturday.
We returned on Sunday and then every day for the next week.
We didn't think it was bad at all. Crowded, yes. Crazy packed, no. What was interesting was the week AFTER felt pretty much like the week before. That surprised us because we thought attendance would drop dramatically, especially since a CM at CSR told us that occupancy there was dropping 50% on the Sunday after Thanksgiving.
The weather was awesome - it literally only sprinkled once during an early morning and was over in an hour or so.
I would go back during Thanksgiving week, but probably only if we also spent the week before or the week after there as well. I was told that last year (2013) the week before Thanksgiving was pleasantly light crowds.
2013 was also an unusual year with the holiday being so late in November; this year I believe the same occurs so if that is true than last year might be a good year to use for forecasting.