Thais celebrate NYE in a big way, so any of those places you mention will be having parties on the beaches, in the bars, at the resorts. But they won't be as full on as KP. I've had a few NYE at Koh Samui and always enjoyed it there. Was at Chaweng for Y2K, that was a blast and a half.
Not too sure about Phuket these days, but there are semi-secluded beaches & bays around Samui. The best way to find them is to rent a motorcycle and do a trip around the island. However, if you have already pre-paid accommodation then you won't be able to just move. I always like the Coral Cove area on the rocks between Lamai & Chaweng. It doesn't get too crowded there and the scenery is fantastic. Also Chaweng Noi and Choengmon beaches are less crowded than Chaweng or Lamai.
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