When staying onsite at Universal, the front-of-the-line pass is an awesome perk. Your waits on every ride are much shorter, and you get early admission to the Harry Potter areas. Highly recommended to stay on site, although I'm guessing it's more expensive. We stayed there last year, did three park days, which was more than enough time to see everything. Teenagers might enjoy the more intense rides at Universal. I have not been during the holidays, but I'm assuming Universal does something.
Disney World between Christmas and New Years is an absolute zoo. The parks have been known to close because they are at capacity. Needless to say, you don't want to be inside the parks then anyway because you can't do anything. Crowd levels at Disney World might drop a little bit starting Jan 1, but maybe not a lot since it's a weekend? Disney has new Fastpass reservation system where you can book ride reservations up to 60 days in advance. Crowds will be heavy, but if you get to the parks early, you can get a lot done the first few hours of the day. The parks will also be open late into the night, popular touring plan would be to go early, take a break during the day, then go back late. With Fastpasses, you could also sleep late, then go to the parks and stay until closing.
If I was going on those days, and wanted to get a taste of everything, I would do 3 days Universal and then 4 days Disney. Check in Dec 29 Universal, you'll have 2 1/2 park days there. On morning of Jan 1, check out and move to Disney World. 4 days you can visit all 4 parks Magic Kingdom, Epcot, Hollywood Studios, Animal Kingdom.