Dry dog food is cheaper and often more convenient. However, canned foods usually contain more protein, and less carbs (which is a good thing, dogs are carnivores). Because of how the cans are sealed, wet foods don't need additional preservatives, and they usually do not contain artificial flavors or colors.
Canned (wet) foods, again because of how they are sealed, actually have a longer shelf life than dry kibbles, despite the fact that they contain less preservatives. Buying lots of cans may take up more space, but if you want to buy dog food in bulk canned foods will last longer when stored, as long as the cans are not opened, than dry food.
The water content in wet foods can help to keep dogs urinary tract healthy, especially if, for some reason, your dog doesn't drink enough water. Also, many dogs simply prefer the taste of wet food over dry.
One plus for dry food is that it usually contains higher levels of fiber, which can help your dog's digestive tract. Some owners report that their dogs have softer stool when fed only wet food.
If I had to choose just one, I would vote for wet food. However, I think feeding a mixture of both is great. It allows for owners to take advantage of the pros of both types of food, and gives the dog a bit more variety in their diet. Also, keep in mind that feeding commercially prepared foods are not the only options out there. There are also home made and raw diets, which many people feel are superior to all kinds of commercially processed diets.