What everybody else said...
It's better for keeping things frozen. It's solid and sublimates (goes from solid to gas without going through a liquid stage) and it expands when it does so. It is CO₂, so try not to inhale it or you'll get dizzy, and wear gloves or you'll flash-freeze your hands.

You won't get wet with dry ice, but I'd think those closed, re-usable blue pack things would be easier on the food.

Also, we used to make our own dry ice for use in mosquito traps as bait when it sublimates. Some mossies are attracted to light, some aren't, but every last one of 'em is attracted to CO₂.

Of course, you can do some pretty cool tricks with dry ice...