Did the vet tell you what grade of LP? Glucosamine is one of several supplements that help rebuild cartilage and restore joint fluid. Concerning the differences between Dasuquin and Cosequin, Dasuquin also has an avocado/soybean unsaponifiables, and a review of human studies found that this showed beneficial effects in people with osteoarthritis.
This article explains some of the differences in joint medications. Also, it tells which brands when tested had none of the claimed Glucosamine and Chondroitin in the product. It's mainly given for arthritis, and if your dog has arthritis, be aware that grains and starchy carbs can contribute to the inflammation, and of course, keep your dogs lean, this helps the joints enormously.
DogAware.com Health: Supplements & Diet Guidelines for Dogs with Arthritis