There's no particular harm in switching diets occasionally, but don't do it for 'variety'. Dogs prefer a monotonous diet -- they're just like little kids in that they'll grab the new and shiny, but don't like surprises in their bowl either. But dogs, like humans, are pretty durn flexible in their diet requirements -- they can do well on a wide range of very unlike diets, are not terribly susceptible to deficiencies, and are usually fine so long as they get sufficient protein and fat (and calories if they're working dogs).
Most commercial dog food is not so perfectly consistent that it's utterly unvarying nutritionally. It differs slightly from batch to batch as the manufacturer cycles seasonally from one ingredient supplier to the next. This is generally enough to address microdeficiencies all by itself.
If a dog has an issue with being on a given diet for a long time, it's usually because that diet has some deficiency or imbalance. (Or occasionally because the dog has a genetic defect, or due to its specific parasite load, particularly giardia.) Back in the 1970s I'd switch between Purina HiPro and Tuffy's (two nominally identical foods) about every 6 months, because that addressed the problem nicely. The difference appeared to lie in the processing of the soybean meal content (which I'd rather not have in pet food, but back then we didn't have a choice) and therefore in the amino acid balance.
Incidentally, lamb (or milk) as the
sole animal protein will cause taurine deficiency in dogs. Just in case you wonder why that dog eating 'non-allergenic' lamb-and-rice itches like crazy all the time... it's not allergy, it's deficiency. MOST so-called 'food allergies' in dogs are in fact due to deficiency or imbalance. Yes, dogs need a little taurine, tho they're not as diet-dependent as cats. Any other animal product provides sufficient taurine.
As a good general rule, the more exotic the diet, the more likely it is to be deficient, often in something you might not expect. I know a commercial breeder who fed all his toy dogs a meticulously planned 'raw' diet and was pleased as hell for 6 or 7 years... when suddenly their toenails started falling off. Turns out this was due to zinc deficiency, which takes years to manifest, but is not uncommon in 'raw' diets. -- Pet dogs have access to human scraps and random dirt/bugs/etc. that kennel dogs generally don't, which is why pet dogs can often get by on a very unbalanced or deficient diet and the owner never knows the deficiency exists.
Price/hype and nutritional quality have little to do with one another. You'd think the most expensive diets would have the most research behind 'em, but it's rather the reverse. In fact one very pricey brand was formulated by astrology, or so the owner says (and consists mostly of mill waste, which explains why dogs fed this crap lose weight and produce mountains of stool). Conversely some 'cheap grocery brands' are very good nutritionally. If a company emphasizes how they're so much better because [mumbo-jumbo] and how everyone else is shit because [they don't do mumbo-jumbo], chances are they're mostly hype. And it's hilarious to see the same product under a different label at double the price... but that's often so with much-hyped diets. A lot of the super-dogfood products are just Diamond Feeds in a tux. (And know where venison in dog food mostly comes from? Roadkill. Montana F&G alone sells 60,000 pounds of roadkilled deer to petfood companies every spring. This is why it has to be listed as an ingredient separate from 'meat' since 'meat' can't legally include roadkill.)
Purina catches a lot of hell, but theirs is the only really
trustworthy nutritional research, because their research and marketing departments have clearly never met. (They often assert completely opposite things.) Or at least so it's always been -- don't know if that will continue under Nestle's ownership. Every other company's 'research' that I've seen has proven to have an agenda -- making themselves look good and others look bad, or sometimes geared toward making good nutrition look bad to save on costs. (*cough*Science Diet*cough*)
Be cautious of websites comparing brands or ingredients. At least one such appears to be a shill for a pet food company (funny how only the ingredients
they use get a pass), and I have yet to see one that knows what the hell it's talking about.
And as a final laugh... people scream about 'byproducts' in pet food, then pay 4 bucks a pound for tripe. Uh, what do they think 'byproducts' ARE, anyway??
Legal definition:
Meat By-Products: the non-rendered, clean parts, other than meat, derived from slaughtered mammals. It includes, but is not limited to lungs, spleen, kidneys, brain, livers, blood, bone, partially defatted low temperature fatty tissue, and stomachs and intestines freed of their contents. It does not include hair, horns, teeth and hoofs. It shall be suitable for use in animal food.
IOW, the most nutrient-dense part of the carcass. But only if you pay 10x as much for it.