If an ice cube floating in a glass of water melts, the water will still be at the same level afterwards.
If a floating iceberg melts, it will add water to the oceans, causing the average water level to be the same.
However, there is still more water in motion, so the effect of the tide will probably be larger.
(Also, I was under the impression that the Antarctic ice wasn't floating? Or maybe this section was?)
I read recently (i think it was on the naked scientist) that these large masses of ice have a small gravitational field. They pull water close to them. When the ice bergs break up, they lose mass and gravity. The article was suggesting that water levels will rise because the water that was pulled by the icebergs will now be in the ocean.