Dry ice is awesome. Very cold. Pound for pound, a higher latent heat of fusion, (sublimation, in the CO2 case) than water! At about 1.7x higher LHF, you only need 8.82 lbs dry ice to do the work of 15 lbs water ice. Cool! Oops, that's wrong, I had it backwards. Dry ice only has 0.55x the LHF of water (184 kJ/kg vs 334 kJ/kg). So you need nearly 30 lbs dry ice to get the same cooling as 15 lbs water!!!!
Problem is, it sucks at cooling water. When you drop dry ice into water, it will bubble furiously at first, with all that water heat going into the LHF of the CO2 and cooling the water, which is awesome. However, soon enough a shell of WATER ice will form around the Dry Ice. The water ice acts as an insulator, with the dry ice cooling it from within....and heat transfer drops precipitously. It will take a LOT longer to cool a given volume of water with a block of dry ice than it will with water ice.
The advantage to dry ice is it is so damn COLD, (-78C sublimation temp, IIRC), which is great for when you need to chill things far below zero, (dry ice acetone baths are awesome in chemistry labs), but not really all that useful for chilling water. Think of it this way - you have a choice between a block of iron at 150*F, or a pin heated to red hot 1500*F....which one is better for heating a room? Greater temp extremes are not always better.
After all that, the takeaway is: Water Ice is better for cooling water.