The week after Christmas is reportidly the busiest week of the year. Saying that we were at WDW last Christmas and New Year (21st December - 2nd January) and it was no where near as bad as what people made it out to be and I would go at that time of year again.
All the christmas parades were still running, as was holiday wishes and holiday illuminations. The Osborne lights were up and the Candle Light Processional was still on in Epcot. We had an amazing trip. I think what made it so good though was the amount of research done before hand. We planned what parks we were going to on what days (avoid morning EMH, instead be at a non EMH park for opening) and made a list of must do's, did those and got out of the parks at lunch time (by this time it was busy but didn't bother us as we were leaving and had already done all we wanted to as walk on's in the morning.) Then we went back to the resort for a swim, toured the deluxe resorts to take pictures etc. We made all our ADR's as soon as we could and booked on a few tours too. We made sure we had a dinner ADR for each day. We spent NYE in MGM as it is the least crowded park (Epcot and MK closed due to capacity) and had a wonderful evening. The park was busy but the atmosphere was great. We made sure we walked through the shops to get to the exit which was really easy and we were back in our room 30 minutes after the fireworks ended.
Have a great trip.