For me, the considerable environmental issues aside, the problem with farmed fish is that it simply doesn't taste nearly as good as the wild-caught versions.
Take salmon for instance. In a lifetime of preparing and then eating several portions of salmon per week, I've noticed that the farmed salmon are pretty much always:
-Very pale pink color, as though the animal was unhealthy (sometimes stores even add red food dye to cover this up)
-Weak and mushy flesh, even when fresh; healthy salmon flesh is muscled and springy, it isn't naturally slimy and it holds its shape
-Weak flavor that seems to be missing a lot of the more robust flavor notes entirely
-Thinner or nearly-nonexistent layer of fat between the flesh and the scales (contributes to less flavor overall and removes a lot of the umami); the same problem also applies to the thin bands of fat between the rows of muscle in the filet itself
-Skin/scales slightly disintegrate or fleck away at a touch instead of remaining intact
I don't even bother buying it even if it's significantly cheaper.
I can't imagine that the nutrient content is the same as the wild-caught fish. And based on the sickly look and taste of the meat, it's also very hard to believe that the farmed fish live a life that they find to be pleasant, to the extent such a thing is possible.