I too agree - - the strong fish taste usually is related to not removing the fat from the fish.  As stated above, the dark looking red stuff is fat and one should strive to remove all of it from the fillet.

Just like people, you can see differences in the amount of fat on fish of the same species.  If one just does the standard fillet & skin job, there can be quite a bit of difference in how much red fat is present right along the lateral line of the fish.  As MT suggested, take the extra time to cut out this section of red meat and you will definitely notice the difference in taste.