We are also going to be at EPCOT for NYE. Each country will have a celebration when it turns midnight in their own country; if you make ADRs for dinner, you will more than likely have to wait 1-2 hours for your table; there are drink stations set-up all over EPCOT; each country will have a band playing; Disney usually passes out hats and noisemakers; I have been people grabbing a spot for the fireworks about 6+ hours ahead; and yes, it is very, very, crowded -- but a lot of fun. I have also waited in line 45-minutes for something to drink (coke, water stations). On the other side, MK is also extremely crowded -- but other than Fantasy in the Sky fireworks there is not "as much" celebrating. The teens will love EPCOT.
You might want to go to EPCOT early in the afternoon and then plan on staying until it closes at 1 am.