This one, admittedly, is a tough one for me to address, due to the reasons that I became vegan.
I’m personally vegan for animal welfare reasons, as opposed to strictly environmental reasons. This means I haven’t had to put a lot of effort into researching the differences between wild-caught and farm-raised fish, since I just avoid eating fish in general.
For detailed info on this, you might be better off touching base with one of those other flavors of vegans. If you’re friends with Al Gore, he can probably explain it better.
A couple things I do know:
For folks who are concerned about the devastating effects of overfishing and by-catch, farmed fish can seem like a good alternative.
However, fish farms do create dire invasive species problems, are potentially really gross for the planet and human health, and can be pretty cruel (see this and this). So if you’re contemplating continuing to support the farmed fish industry, you’ll probably want to look into it further.