Hi Ramya, I'm new here, so I'm very happy there's a subject I can actually contribute to I spent last between-Christmas-New Year's Eve break in the Copenhagen.
Pros: you get to experience the amazing Christmas atmosphere, decorations et all, Tivoli is a fantasy and Torvehallerne looks even more delicious than usual. Plus, Copenhagen is a beautiful, if a little cloudy city - definitely worth seeing
Cons: it's hard to enter some museums/galleries and even shops (either that or they close really early) and the ratio tourist : locals is probably higher than usual. Oh, and if you're interested in going out for the Christmas or New Year's dinner, better book now. We spent hours looking for a decent restaurant to dine and ended up at kebab bar.
Good luck!