While dry dog food (commonly called kibble) is cheaper and more convenient, wet dog food (also known as canned food) contains more protein and provides better hydration.
Dry dog food is made up of 18-32% protein, 8-22% fat and 46-74% carbohydrates. Wet dog food is made up of 28-50% protein, 20-32% fat and 18-57% carbohydrates.  The higher protein content in wet dog food is a definite plus, especially for puppies and young, growing dogs.
edit Ingredients in wet vs dry dog food
Dry dog food contains synthetic preservatives. It tends to be high in gluten and can be sprayed with animal fat.
Because wet dog food comes in sealed cans, it does not contain synthetic preservatives or artificial flavorings or colorings. It also contains more moisture, which is good for hydration and the urinary tract.
Wet or canned dog food is generally more expensive than dry food. For example, while 15 lbs of Pedigree Healthy Weight dry food is $12.24 on Amazon.com, 24 3.2-Ounce Cans meals of Pedigree Choice Cuts canned dog food costs $17.78 from the same store.
Dry dog food is more convenient to store and serve, as it comes in bags and can be left in the dog’s bowl for an extended period of time.
Wet dog food must be refrigerated after it is opened and must be used within 2 to 3 days. It should not be left in a dog’s bowl for more than two hours. Cans have a long shelf like when left unopened.
edit Suitability for Puppies
Puppies tend to do better on wet dog food because it has added hydration and is easier on their teeth.