Eating sustainable seafood is (and has) been gaining in popularity over the past few years as more people have taken an interest in how their food gets to their plate and the potential harm to the environment. There is no absolute answer to the question “Is wild better than farmed?”. It depends on both the fishing and the farming practices.
One of the most common fishing methods in the US is trawling. In this practice large nets are towed behind boats to catch fish or shellfish. They can be dragged in the middle of the water or along the sea floor, with the latter resulting in large levels of bycatch (most of which don’t survive, even if they’re tossed back). The second most popular method is purse seining, which catches large schools of fish all at once. One of the best fishing practices is pole/troll, which uses a traditional pole and bait method to catch fish one at a time. The Monterey Bay Aquarium has a complete list of fishing and fish farming methods along with their levels of popularity.
The Environmental Defense Fund also has a good article about fish farming and which practices are most harmful. Some of the biggest problems are polluting surrounding waters, depleting wild fish to feed farmed fish (and getting fewer farmed fish in return) and possibly introducing new risks to wild fish if the farmed fish escape.
How can you help protect fish stocks from being depleted? Simply look at the lists put together by the Monterey Bay Aquarium and Blue Ocean Institute to see which fish are sustainable and which aren’t. Blue Ocean also notes fish high in mercury. Both sites have wallet size brochures for fish and shellfish and a separate card for sushi. Seafood Watch, part of the Monterey Bay Aquarium, also has a free iphone app. The easiest way for you to impact which fish are caught, and how, is to decide what you want you want to spend your money on. Without demand, there won’t be a supply.