I don't know anything specifically about Science Diet, but here is a really good website about dog food:
http://www.mordanna.com/dogfood/ - this website talks about what ingredients to avoid in foods and which ones are better, etc.
I know there is a lot of controversy over Science Diet because supposedly this company pays/gives scholarships to vets. In return, they sell their products at their clinic. I have NO idea if this is true or not. I know a lot of vets sell Science Diet because they have an extensive line of prescription foods.
There are a lot of ingredients that can cause allergies in dogs, including animal protein. However, it is my understanding that allergies in dogs don't show up until they are at least a year old, so you probably won't know if its causing problems for a long time.
When I first brought Brody home at 12 weeks, he was itching like crazy, including his face which is a sign of allergies. The breeder had been feeding him Purina Puppy Chow. After I did research (a lot of research) on dog food, I realized that Purina Puppy Chow is NOT good. I think Science Diet is a step up from Purina Puppy Chow, but I don't think its top of the line. The reason that dog foods vary in price is not because of the amount of protein, but because of they type of protein. Some dog foods use by-products (avoid these) while other dog foods use more quality proteins that humans would also eat.
I just looked up the ingredients for the Science Diet Puppy food and the first ingredient is Ground Whole Grain Corn and the second ingredient is Chicken By-Products Meal. I looked up Science Diet Nature's Best for Puppies and it listed Brewers Rice, then Chicken Meal. This sounds a lot better. However, it also lists animal fat, which is bad. I couldn't tell from your post which one your feeding. Here is the website for Science Diet Puppy foods:
http://www.hillspet.com/zSkin_2/prod...=1122749837746
Compare ingredients listed to the ingredients at The Dog Food Project's website that I gave you above.
What I did when I was trying to find a dog food was I went to Petsmart's website (my local pet store) and I figured out every food that was available there. Then I looked up the ingredient list for every food. I compared the ingredient lists to what I had read about what avoid and look for in a dog food. I know it sounds like A LOT of work, but for me, it was worth it. You might also go to the library and look for books about dog nutrition. My library has a ton of these books. There is usually a chapter about what to look for in a dog food.
I decided to feed Brody Royal Canin. This is definitely not the "best" food on the market. However, they sold it locally so I knew that I would always be available. There are a lot of other products that sell organic food, which is probably the best choice, but its just not available to me. Also, Brody really likes Royal Canin Mini Puppy Food. I am also a sucker for the marketing they have where they make a food just for Yorkies. Here is the Royal Canin's product website:
http://www.caninehealthnutrition.com/miniproducts.html
I don't advocate Royal Canin, its just what Brody eats. I previously owned an Akita and he pretty much ate the WalMart brand of food because my family never realized that dog foods varied so greatly - it just seemed like dog food is dog food. He lived to be 12 years old, which is old for an Akita. My point here is that in the long run, the dog food you choose will probably not cause major health defects. However, a dog food with the right ingredients might help your puppy look and feel better. I personally think the absolute most important aspect of dog food is that your dog likes it and seems happy! She doesn't care about the ingredients.
I would like to stress that I am NOT an expert on any of this. I just wanted to share the research that I've done. Sorry for the long post!