Being on a cruise for New Year's Eve is imho one of the very best nights to be on a ship.
Everyone is out and about and partaking in the fun celebrations. The mood is good, and everyone is out to enjoy themselves.
The only drawback is the rest of the days and nights during a cruise over New Years, and the fact you pay a fairly steep premium for cruising then.
On Xmas and New Year's cruises there are LOTS of people, as they generally sail OVER full, as there are lots of families; meaning lots of cabins holding 3 and 4 people.
On a ship like Independence you'll have at least 1500 under 18s, I'd bet. With that many "kids" onboard I think the other days and nights are adversely affected.