Some of the restaurants do change their menus or add special items during the holidays. The big difference seems to be that buffets increase their prices to reflect "holiday pricing" at that time. (Not just Christmas Day, pretty much the whole holiday season.) You can go here
http://www.wdwinfo.com/holidays/Christmasdining.htm to see how it worked last year.
I've never been on Christmas day, but I have been there for NYE/NYD and my advice would be to pick a restaurant based on where you're going to be that day. The crowds are so crazy that you really can't hop (or go back to a resort) with any real guarantee of getting back in to the park you want. Some people hit the timing just right and manage to leave/re-enter the park they chose, but it makes me nervous, particularly if you want to be at MK.
At the MK, I'd probably pick Crystal Palace for a large group. Lots of choices and a nice setting. Lovely decorations, too. If you were at Epcot, I'd probably go for Chefs de France. At MGM, Brown Derby for a nice meal. Otherwise, you might look to see what your resort offers in terms of restaurants, in case the crowds don't appeal to you and you don't intend to be in a park.
Whatever you do, make sure you call as soon as you're able to make ADRs and get something reserved. And I strongly recommend visiting the WL and the GF to see the decorations during your vacation - even if you don't eat there.