It's an unfortunate (but pretty well known) truth that most veterinarians receive little nutritional training during their time as students. And even greater problem is that what little training they get is from representatives from Science Diet, Royal Canin, Purina, and Iams. So what do you think they will recommend? The only thing that they know anything about. Vets that care to educate themselves can find a wealth of information available to them through other sources. My vet is one such vet, and he highly recommends TOTW to any client who has a dog that gets ear infections, skin infections, is itchy, has stool or stomach issues.
I feel that you should do your own research and form your own opinions, rather than believing what you are spoon-fed by vets (who may or may not have a clue about nutrition) or what you are told on a forum of non-professionals (for the record, I have worked extensively in the veterinary field and have many colleagues who are currently in vet school or practicing veterinarians). So I'm going to provide you with some information and resources and I would strongly urge you to do some research and form your own opinions about what is best for your dog. Also for the record, Royal Canin is EXTREMELY overpriced for a not-so-high-quality food (low grade ingredients and cheap fillers).
This will be long. Bear with me.
Royal Canin was established in 1967. They are owned by Mars, a large food product manufacturer (one of their more popular products is a well known candy-bar brand). They manufacture lots of things other than pet food, and a lot of their "byproducts" from the products marketed at humans go into their pet food line. They were involved in the high-volume pet food recalls of 2007 due to melamine contaminated kibble. One of their biggest marketing ploys is advertising pet food that is "breed" specific (this causes me to shake my head every time I think about it). Royal Canin is based out of France. List of recalls since March 2007:
List of recalls for Pet Food Products from Royal Canin
Diamond Pet Foods (manufactures TOTW) was established in 1970 (what was that your vet said about long-running?). TOTW is a newer product line by a well established company (RC comes out with new product lines yearly; this is common). This company also produces Solid Gold, Canidae, and several other high quality dog foods. Compare to RC which uses corn in most of their products. Diamond Pet Foods is based out of Missouri, with plants in various states in the US. This company solely manufactures pet food. They were involved in a low-scale recall in 2005 due to aflatoxin contaminated kibble. Here is a list of recalls since March 2007:
List of recalls for Pet Food Products from DIAMOND
May I add that TOTW is much higher quality for significantly less cash. Now, I chose to just compare these two particular companies here since they were the ones in questions. There is a WEALTH of information out there on both of these companies, as well as many many others. I will end by providing you with some extra reading to begin you on your quest to become more knowledgeable about pet food.
The Dog Food Project - How does your Dog Food Brand compare? -- excellent site to explain all of these things I have talked about, how to read a label, ingredients to be cautious of, etc.
Dog Food Analysis - Reviews of kibble -- great for comparing kibbles to each other.
Complete and Final.doc - 4shared.com - document sharing - download -- file to download. If you read nothing else, read this. It's long, but is very concise, well written, and easy to understand.
So do your research and YOU decide what's best for you dog. No one here can tell you that, and honestly your vet can't either. They just simply (and tragically) don't get enough training in this field by unbiased sources to be reliable. That is,
unless they take initiative to go beyond what they are provided in vet school and educate themselves.
ETA: I am not familiar with NutriSource but at first glance it appears to be a decent food (much much better than RC). So if she will eat that, I say stick with it. Still won't hurt for you to read up on it though. That way you will know WHY it's better than RC.
ETA, again: Some varieties of Nutrisource contain menadione sodium bisulfate complex, a synthetic source of Vitamin K with many known (sometimes lethal) side effects. I would be wary and read labels very carefully.