Epcot for New Years Eve is my absolutely favorite place to celebrate! Such a fun time! I have been 3 times and the atmosphere is exciting and energetic, but different from what you will find at Magic Kingdom. A few of the countries will host dance parties that you can check out (usually it's China, Germany, Morocco and one other, Canada, maybe) and in the past they have given out hats and noise makers at the entrances. Epcot typically does 2 shows: 1 at 7 or 8 pm and another at midnight. Illuminations with the Holiday finale play before for midnight celebration (which I think is epic!).
The crowd tends to be older and most cast members who don't have to work will head to Epcot to celebrate. When we went we staked out our spot pretty early because we knew we weren't going to get much, if anything, done and enjoyed the people watching and conversations. We took turns getting drinks and bringing them back. The lines for drinks and bathrooms are long, so be prepared to wait longer than normal. Patience is a virtue on this night no matter where you are at WDW.
We had an early ADR, between 7-7:30 in anticipation of the long night. Epcot has the highest capacity of all the parks and rarely closes. I believe I have only heard of it reaching capacity twice, so it's a great choice for celebrating the New Year.