We did EPCOT last New Year's Eve and had no problems. It was very crowded, but no problems. We had an ADR for dinner at 7:30, and then walked around (and it was pretty cool - they had alternate paths opened so we walked back to FW in between Norway and Mexico, then under Test Track). Lines were long but manageable. Actually rode Imagination with no wait, which is not unusual).
Spead out a Blanket by the lagoon around 9 and hung out, playing cards and video games. Fireworks were amazing.
I would stay away from MK. Christmas Day (yesterday) it hit capacity shortly after noon and they were turning away everyone who did not have a resort room key. It reopened later - and then the storms came...