Neither food is good, IMO, but definitely stop the HA. A lot of dogs are allergic to corn and/or soy, and HA has both. The LA isn't great either as the first ingredient is rice, and not even whole rice but a byproduct of rice.
Check out a few examples of more holistic allergy choices and compare the ingredients with yours:
Solid Gold Wolf King:
Bison | Salmon Meal | Brown Rice | Millet | Cracked Pearled Barley | Oatmeal | Rice Bran | Canola Oil | Flaxseed Oil | Garlic | Amaranth | Blueberries | Yucca Schidigera Extract | Carotene | Choline Chloride | Vitamin E Supplement | Iron Proteinate | Zinc Proteinate | Copper Proteinate | Manganese Proteinate | Potassium Iodide | Thiamine Mononitrate | Ascorbic Acid | Vitamin A Supplement | Biotin | Calcium Panthothenate | Selenomethionine | Pyridoxine Hydrochloride | Vitamin B12 Supplement | Riboflavin | Vitamin D Supplement | Folic Acid
DVP Natural Balance Sweet Potato and fish:
Sweet Potatoes, Salmon, Salmon Meal, Menhaden Fish Meal, Canola Oil (preserved With Mixed Tocopherols And Citric Acid), Sweet Potato Fiber, Dl-methionine, L-lysine, Sodium Chloride, Salmon Oil, Flaxseed Oil, Rosemary Extract, Natural Flavor, Yucca Schidigera Extract, Potassium Chloride, Choline Chloride, Vitamin E Supplement, Ferrous Sulfate, Zinc Proteinate, Copper Proteinate, Potassium Iodide, Thiamine Mononitrate, Manganese Proteinate, Zinc Sulfate, Copper Sulfate, Manganese Sulfate, Ascorbic Acid, Vitamin A Supplement, Biotin, Calcium Pantothenate, Manganese Sulfate, Sodium Selenite, Pyridoxine Hydrochloride (vitamin B6), Vitamin B12 Supplement, Riboflavin, Vitamin D3 Supplement, Folic Acid.
(That one has more potato than fish though, not as good, IMO).
Timberwolf Organics Ocean Blue
Low Ash White Fish Meal, Salmon, Potatoes, Sardine/Mackerel/Anchovy/Tuna Oils, Kelp, Alfalfa Leaf, Potassium Chloride, Carrot, Watercress, Spinach, Celery, Parsley, Fennel Seed, Blueberries, Cranberries, Pears, Figs, Thyme, Anise Seed, Ground Cinnamon Bark, Fenugreek, Garlic Pieces, Sunflower Seeds, Sesame Seeds, Apples, Taurine, Spirulina, Choline Chloride, Lecithin, Probiotics: (Lactobacillus Acidophilus, Lactobacillus Casei, Lactobacillus Lactis, Bacillus Bifidum, Streptococcus Diacetilactis, Bacillus Subtillus), Taurine, Mixed Tocopherols (a source of vitamin E), Lysine, Zinc Proteinate, Iron Proteinate, Manganese Proteinate, Thiamine, Methionine, Carnitine, Niacin, Vitamin A Supplement, Calcium Pantothenate, Riboflavin Supplement, Vitamin B12 Supplement, Iodine Proteinate, Vitamin D3 Supplement, Biotin, Folic Acid, Pyridoxine (a source of vitamin B6), Copper Proteinate, Selenium Proteinate, Cobalt Proteinate, Papain, Yucca Schidigera Extract.
Do you see the difference? And these foods probably won't cost you more than what you are paying for the special food from the vet.