4 years ago, the AP blockouts didn't make such a big difference as they do today. If I recall correctly, it was really summer 2009 when a huge number of AP holders coupled with perhaps a few new offerings in the park and pending summer blockout periods led to unusually huge crowds for a couple weeks in June, when a lot of AP holders wanted to get a visit in before they were blocked for a couple months. Ever since, people have looked to blockouts as periods the parks will NOT be crowded, which is at least sometimes true.
Blockouts are odd in that they are days that Disney expects to be crowded, so they block some or most AP holders from visiting those days. Sometimes blockout days are surprisingly light (some people last year were surprised at light crowds July 4th, though I'm not so sure about this year). Sometimes blockout days are still crazy-crowded (week after Christmas, for instance). Thanksgiving week seems to vary, but the last couple years it sounds like the days BEFORE Thanksgiving are more crowded than the days immediately AFTER, simply because of the AP blockouts.
That said, in the SAME thread about the days after Thanksgiving, I've heard some people say it was wonderful, some say it was crowded but not awful, and a few even say it was awful. I think a lot of the crowd size is what you're used to, as well as luck (you might just happen to hit what is crowded or not and that would color your perceptions).
I like to plan for the worst but hope for the best. In times I've expected low crowds I've been disappointed. In times I've expected high crowds, they've never been as awful as I pictured (though I've never been New Year's Eve

). In fact, 2 of the 3 trips I went expecting high crowds, we did not find the park crowded at ALL. (And one of those was, of all times, World of Color opening weekend.)
Have a great trip!