We spent NYE in Epocot in 2000/01, and lived to tell the tale
Yes, it was busy, but we had a great (very long) day and evening there. We knew it would be busy, so had nothing specific planned (other than meals) so that anything we could do would be a bonus.
As gilld said, the parks are often full very early (we arrived by 7:30am

), so you do need to be up-and-at-'em if you want to be sure of getting in your park of choice. This also means you won't necessarily get back in to the parks if you want to go back for a rest mid-afternoon, which makes for a very long day indeed if you stay the duration!
In the evening it's great to visit the different countries at the time their 'homelands' are celebrating midnight - this way you get a different NYE on the hour, every hour!

We'd planned our PS in the Rose and Crown so that we could join in with the UK celebrations at 7:00pm (midnight back home). There was also an extra showing of Illuminations around then which hadn't been advertised - a great bonus.
We have never been quicker at getting back to our resort than after the NYE celebrations - one of the CMs said "If there's a bus in Orlando with gas in it, Disney have hired it", and I believe them! From leaving the lagoon in Epcot after an extended Illuminations, to getting back in our room at ASMo (picking up a mug of hot chocolate on the way

) took no more than 45 minutes.
Our DDs were teenagers when we went, and I think I may have planned things differently if we'd had smaller children with us, but Epcot worked well for us
