We were in the parks last year over New Year's and it was our first visit during one of WDW's busier seasons. We found that MK was very crowded on both days that we visited, but the other parks were all quite manageable. We were expecting large crowds on New Year's Day, so we headed to Epcot and didn't think it was terribly crowded at all. On NYE when we expected the worst crowds, we headed to AK, because we planned to spend the evening hours outside of the parks, and AK was quite reasonable, too (being the only park that closed early that night - around 5:00 p.m. I think). The AK strategy might not have worked if we had planned to spend the evening in one of the other parks, though. You might also be interested to know that any PSes we made on the 31st and 1st had to be held with a credit card, and were subject to a $10 per person "no show" charge unless they were cancelled 48 (24?) hours in advance.
You know we had a great time, because we're heading back this year on exactly the same date!