If you have food and water in the run, you don't need either in the coop unless the chickens aren't let out of the coop fairly early in the morning to have access to the food and water.
Some pros of having food and water exclusively in the run: 1) spilled food and water don't end up in the coop, where they should have to be cleaned up, and 2) water doesn't add to coop humidity (especially in winter when frostbite is a risk).
Some cons of having food and water in the run: 1) wild birds may attempt to access food in the run unless it is designed to exclude them, 2) food needs to be secured (e.g., brought in the house) every night to keep rodents from eating and contaminating the food with their droppings, and 3) food needs to be protected from snow and rain so it doesn't get wet and spoil.