They'll probably flux.
AK's crowds this year will be the big factor - how long they stay at AK before choosing their secondary park. They've got big reasons to stay there longer then usual.
Typically though MK will get all ickey around 10am-Noon, but then reopen a few hours later.
This, depending on how things go.. can either sending Epcot into trouble.. or as it has some years, actually boost AK moreso so it goes to phases.
Epcot usually manages to hold their gates, just because of its sheer sizes (plus they makes everyone and their grandmother work NYE - all the internationals and CPs plus all of epcot's normal CMs.. no one really complains because they want to see the fireworks
)
But i digress.. I've seen Epcot start phasing at around 1pm in the afternoon before on a holiday. But, the 3 o'clock hour is when crowds usually start to die down as people exitting is higher then people entering. That should hold for a few hours, but since it's NYE, they should kick back up around 6pm. I think around the 4th of July (similiar style holiday), crowds really started to get thick around 7-8pm.
Now, depending on how crowds flow from AK, and if MK phases early or late, and if AK phases, Epcot can either stay its usual "not too terrible" self, or it could actually start seeing some closures. MGM's really not a consideration this year though.
Epcot does have high word-of-mouth for NYE though, so expect it to be very busy.