In general it is assumed that the energy that is required to produce a certain type of food is a good surrogate for the total environmental burden of food products. I scanned some studies to compare fish and meat (such as poultry, pork and beef) products, however there seems not to be a common consensus:
Energy use for fish (cod and plaice) is higher than for meat (pork, chicken, beef) though the impact on global warming for fish is roughly the same as for pork and chicken. Beef is worse. 
Chicken performs better than filleted fish (salmon from aquaculture and cod) in terms of energy consumption. 
Meat from fish has lower energy requirements than poultry and pork (Data from mid 1990s in the Netherlands). 
Red meat causes around 150% of the greenhouse gas contributions compared to chicken and fish (focused on USA). 
While the first two studies compare only a small range of products the other two are localised (and study  is probably outdated). Are there more general studies or a consensus that I am not aware of?
Which food product chains require more energy? Fish or meat?
 Burg SWK van den, Taal C, de Boer IJM, Bakker T, Viets TC (2012): Environmental performance of wild-caught North Sea whitefish - A comparison with aquaculture and animal husbandry using LCA.
 Ellingsen H, Aanondsen SA (2006): Environmental impacts of wild caught cod and farmed salmon - A comparison with chicken. Int. J. Life Cycle Assess. 11, 60–65.
 Dutilh CE, Kramer KJ (2000). Energy consumption in the food chain - Comparing alternative options in food production and consumption. Ambio J. Hum. Environ. 29, 98–101.
 Weber CL & Matthews HS (2008): Food-Miles and the relative climate impacts of food choices in the United States. Environ. Sci. Technol. 42, 3508–3513.