Pieces of ice added to a drink cool it much faster than ice cold water added to it because
Ice pieces at 0°C do not possess latent heat of fusion, whereas water at 0°C possess latent heat of fusion
Ice pieces at 0°C do not possess latent heat of fusion, whereas water at 0°C possesses latent heat of fusion. Therefore, ice will absorb more heat from drink during melting as compared to water. That is why, the cooling it is better with Ice.