From our Seafood Fabrication class, I've picked up a lot of useful information about the muscular structure of fish and the effect on eating quality.
For example, sole and halibut are flat fish (both eyes on the top side of the body!) that lounge around the ocean sea floor, getting very little exercise. The fact that flat fish are such couch-potatoes means their flesh will taste very mild and will pick up the flavor of any accompanying sauce. For this reason, halibut makes it way onto many restaurant menus.
On the other hand, high activity fish (long distance swimmers like swordfish, salmon and tuna) have very developed muscle structure and highly vascular flesh. Consider the rich maroon color of ahi tuna, or the vibrant pink-orange of salmon; these fish migrate thousands of miles and their flavorful flesh proves it. Flat fish will be comparatively lean because they don't need energy reserves, while high activity fish will be rich in healthy fats and Omega 3s.
One fish with remarkable fat content is escolar, occasionally seen on specialty seafood or sushi menus. Despite escolar's novelty, even the most intrepid eater should skip it. The human stomach cannot digest the chemical structure of the fat in escolar, meaning it causes upset stomachs and other digestive problems (ahem) shortly after eating. Instead, try toro, the fatty belly of ahi tuna. The Japanese market pays top dollar for toro, so it's rarely seen here. Occasionally, toro does make its way to the U.S. If you see it on a menu, ask for a sashimi or nigiri portion- it's beyond delicious!