The ingredients are slightly different between the two, but I think the biggest difference might just be between the companies. Mazuri is a huge company (they are actually now owned by Purina now) they make foods for almost every exotic animal, not just domestic animals but zoo animals too, All Products
where as Oxbow just focuses on small animals. So basically Oxbow is more specialized, as well as they grow at least some of their own ingredients like hay, which gives them better control over quality. Also it could be at least in part simply greed, they "specialize" in small animals so they are going to charge more because they can (I don't know that for sure just guessing).
Mazuri Chinchilla Diet
Dehydrated Alfalfa Meal, Dehulled Soybean Meal, Wheat Middlings, Ground Timothy Hay, Ground Soybean Hulls, Ground Oats, Dried Plain Beet Pulp, Ground Flaxseed, Cane Molasses, Dicalcium Phosphate, Wheat Germ, Soybean Oil, Dried Whey, Salt, DL-Methionine, Calcium Carbonate, Dried Lactobacillus acidophilus Fermentation Product, Dried Lactobacillus casei Fermentation Product, Choline Chloride, Dried Bifidobacterium thermophilum Fermentation Product, Pyridoxine Hydrochloride, Dried Enterococcus faecium Fermentation Product, Folic Acid d-Alpha Tocopheryl Acetate (Vitamin E), L-Ascorbyl-2-Polyphosphate (Vitamin C), Vitamin A Acetate, Magnesium Oxide, Cholecalciferol (Vitamin D3), Manganous Oxide, Zinc Oxide, Calcium Pantothenate, Ferrous Carbonate, Copper Sulfate, Nicotinic Acid, Vitamin B12 Supplement, Riboflavin Supplement, Zinc Sulfate, Calcium Iodate, Sodium Selenite, Cobalt Carbonate.
Oxbow Essentials Chinchilla Food
Alfalfa Meal, Soybean Hulls, Soybean Meal, Wheat Middlings, Soybean Oil, Salt, Lignin Sulfonate, Cane Molasses, Calcium Carbonate, L-Ascorbyl- 2-Monophosphate (Vitamin C), Sodium Bentonite, Hydrolyzed Yeast, Choline Chloride, Vitamin E Supplement, Yeast Culture, Zinc Sulfate, Zinc Proteinate, Niacin, Copper Sulfate, d-Calcium Pantothenate, Manganous Oxide, Riboflavin Supplement, Biotin, Thiamine Mononitrate, Magnesium Sulfate, Copper Proteinate, Vitamin A Supplement, Sodium Selenite, Manganese Proteinate, Pyridoxine Hydrochloride, Folic Acid, Vitamin D3 Supplement, Cobalt Carbonate, Vitamin B12 Supplement, Calcium Iodate