Pet nutrition is very important. Its also a bit subjective. You could ask 10 people what food is best and you will get 10 different answers. This is my opinion. It is based on 20 years of research and experience, but it still just my opinion.
First of all..and this may sound odd, but your vet isnt always the best person to ask what to feed your pet. I've worked with MANY vets who knew nothing about nutrition and the little they did know was from the 2 or 3 classes they took on it in school. Classes that are argued by many, are bought and paid for by the big 3 of prescription pet food. (Purina, Science Diet and Royal Canin).
Just like every person has different dietary needs, so do dogs and cats. What is perfect for one may be extremely unhealthy for another. To put it in human terms...I have several friends who have done the Atkins diet with great results. I couldn't do it without putting my health at great risk because I was born with pancreatitis and have to keep my protein and fat intake to a minimum. All that meat on the Atkins diet would put me in the hospital writhing in pain! But they lost weight and felt great. Same with dogs and cats. There is no one perfect food.
Having said that...do your research. Pretty much any dog or cat food that you can buy at the supermarket is garbage. It is the nutritional equivalent of you eating nothing but McDonalds all day every day your entire life. Yes you could live and some people may actually stay healthy against the odds...but it certainly isn't recommended.
Personally, I feed my dog Blue Buffalo. It is a grain free diet that is great for his coat and health. I've had dogs with serious allergies (one that would claw himself bloody even on meds) and a few weeks on BB and the itching was down by @85%!! So I am a big fan. And it isnt very expensive! I pay @ $18 for a bag of dry and $2-$2.50 a can. My 13 pound dog will eat 1/4 can a day and the smallest bag of dry(which is the $18 one I get) lasts well over a month. I dont give him canned every day...about 4x a week. So 1 can lasts him a week. So less then $26 feeds my boy with high quality food for a month!
I feed my cats Science Diet original dry. I'd love for them to eat Blue Buffalo as well but my female will not under any circumstances eat anything BUT SD original dry. She is 10 years old and unlikely to change. I've tried many times. She flat out refuses to eat (and while a dog will eat on its own eventually, it can be very dangerous to let a cat go on refusing to eat as they will be stubborn enough to starve themselves right into kidney failure) and runs back and forth over our heads all night to show her displeasure. So SD it is! A smaller sized bag is @ $19 and lasts me (feeding my 3 cats and occasionally a stray) almost a month. And my cats can EAT! I give my boys some canned once in awhile, but not every night and my girl refuses to eat canned. (yes she's a diva and yes she rules the house!)
They are all as healthy as can be!
Birds are the opposite of cats and dogs in that the more healthy people food they get the better. Mine get a bowl of seeds & pellets to nibble all day, but also get plates of people food. They love organic spring mix salad mix. They also get some of whatever I make that day that's good for them...veggies, fruits, grains...tonight they will get some mashed potatoes and broccoli. They had some cereal for breakfast and a big plate of salad for lunch. The phrase "eating like a bird" was obviously made up by someone who had never had to feed the little piggies!
So the bottom line is...do your research and get the best food you can. Lots of the problems we see in the vets office (allergies, kidney and liver failure, dental problems, etc...) could have been helped immensely or even avoided all together by feeding the right diet from the beginning!