Thanks for posting – this is a really good question and seems to come up on Yahoo Answers frequently.
My first advice would be not to listen to your vet when it comes to nutrition. Veterinarians receive very little instruction in regards to nutrition when they are at school, and what they receive is often sponsored by the big pet food companies – so of course they will recommend Eukanuba, Purina, Science Diet, etc.
My second advice is, learn more about dog food. There’s a great site called the Dog Food Project at http://www.dogfoodproject.com/ , which has information about all the ingredients in dog food and how to choose a food that is of good quality. I would start there.
Personally, neither Eukanuba nor Purina Pro Plan are what I would consider "good" dog foods by a long shot. They are commercial grade dog foods that are produced cheaply and are full of fillers (corn, wheat, etc.) and other unnecessary things (sugar, food coloring, etc.) that your dog doesn’t need.
You will want to look for a higher grade commercial kibble, or a premium grade kibble. Some good kibbles they sell at the pet food chains are Natural Balance, Nutro Ultra, and Blue Buffalo.
If you have a specialty pet store nearby, you should be able to get a hold of premium grade kibbles, or you can order them online. Recommended, good foods are Timberwolf Organics, Canidae, Solid Gold, California Naturals, Innova Evo and Fromm’s.
You may also want to consider a nutritional supplement that promotes a healthy coat and healthy skin. You can give Salmon Oil in liquid form, or Fish Oil pills (I like the combination fix, flax, and borage oil ones). You can purchase both at the grocery store in the human supplements aisle.