We love the nutritional benefits of fish, but unfortunately, farmed fish lack a significant amount of the nutritional benefits that we associate with wild catch. The difference in nutritional value is due to their food source. While wild fish consume their omega-3s from aquatic plants, farmed fish are fed with a high-corn diet. This causes farmed fish to accumulate unhealthy levels of the fatty acids (which you can see in the thicker fat deposits of a salmon filet, for example).
Additionally, farmed fish are often given antibiotics, which can cause humans who eat farmed fish to develop antibiotic-resistant disease. Then there are the ethical questions to think about in terms of farm fishing. Farmed fish are subjected to the routine stresses of hyper-confinement and are typically killed in slow, painful ways.