We're arriving the same day as you! There has been a few posts about this and consensus seems to be that Jan 2 will be fairly busy but alot quieter than NYE as people will already be heading home to start school/work on the 3rd.
By Monday, the parks will be dead. As for parks being busier than each other, I would avoid MK (just a hunch that people will want to say goodbye before they leave) and head for Epcot as this park has never been known to close its gates on NYE which can be the busiest day. Therefore, the capacity is probably larger and will cope better with crowds.
We are heading for Seaworld on the 2nd as this park is quite good at spreading crowds (big audotauriums) and will hit WDW on 3rd. What about Disneyquest or a shopping day if you're nervous about crowds? Or maybe a character meal to set the mood (planning a PS to Chef Mickeys on the 2nd, maybe we'll see you there)
Decorations will still be up and jan 2nd is the last day of Osborne Lights at MGM so maybe this is worth a look, they are spectacular! All the resorts will still have decorations up for the first week of Jan. Try the resort board for more details of this, but these resorts are really worth a look as well. Gosh, I'm gushing, aren't I?
Anyway, sorry for waffling and hope I have been some help. Look out on the meet board for possible January meet-up if interested,
Much pixie dust,
Claire