It depends on what kind of brine you are feeding the fish. If it from a fish store, it is an adult brine shrimp (larger species of brine shrimp.) The only brine shrimp with nutritional value is baby brine shrimp (also called napulii). Baby brine are nutritional to a fish because the newly hatched brine contain a large drop of oil which is highly nutritious. This is rapidly depleted as the shrimp grow, and their nutritional value declines rapidly a few hours after hatching. Thus, when they get to the adult stage, they pretty much have depleted any nutrition that they had.
Frozen is nutritional however because not only is it purified to eliminate any risk of disease transfer, but these frozen food companies have biologists who test products again and again to make the most nutritious formulas possible, enriching each with different ingredients until they find a formula that is most nutritious for fish's health, growth, and coloring.
The only downside in feeding frozen is that frozen will decay in the tank if not eaten or removed, whereas a live food will not.