Honestly, I've been probably 20 times around New Years and it's always pretty crowded, but worse on 12/30 than like 12/26 or 12/27.
I think some people leave after Xmas and a new crop comes in those final 3 days for New Years. For me, 12/31 is by far the most crowded feel I've experienced. Worse than July 4, worse than Easter, worse than Thanksgiving, and worse than Xmas day.
I was there for the Year 2000 and it was insane. Somehow, I think that was more crowded than any time I've ever seen the parks. I think MK closed to new guests at like 9am.
Around January 2, it drops off like a cliff.