I've been several times at new year and have never bothered with any of the shows - the atmosphere in the park is great fun, so that was enough for us. The Central Plaza is set up as a sort of huge disco, so if you want to dance and party with loads (and I mean huge crowds) that's the place to be. This is where the main countdown takes place, and is a great spot to watch the fireworks over the Castle. Of course, the rest of the park and all the attractions are open, often until 2 or 3 in the morning.
If you are daunted by large crowds, or have little ones it might be better to not get stuck into the middle of things, and you will have to be prepared for a slow exodus from the park at closing time. Other than that, I can thoroughly recommend new year at DLP.
Regards
Rob