I've been on a couple New Year cruises and other than a countdown party on New Years eve with free champagne for an hour or so, and the leftover Christmas decorations, there isn't much else that makes it any different from other cruises. Too many people book them thinking it is one big party every day and night and the truth is, it isn't. You may see more guests wearing tuxedos and evening gowns on New Years eve. Of course the price is higher too.
I do not plan to book another New Years cruise.