Wild caught fish are less likely to have diseases compared to farmed fish. However, when they have diseases, they are unusual ones and quite often involve parasitic worms that belong in goats or other animals and get lost in the fish's body.
Wild caught are generally stronger and healthier overall but they need to be kept in water that has the same pH, GH, KH and temperature to what they find in the wild. Farmed fish will usually tolerate a little more variation in their water chemistry and temperature.
Wild caught don't normally take dry food (especially floating foods) and usually require live or frozen foods. Sometimes they will learn to take dry foods but don't count on it.
Wild caught are quite often harder to breed in captivity but if conditions are right, they are easy to breed.
Wild fish usually have better colours but it depends on if you want original colours or man made mutations.
Ethical concerns, everything we do has ethical concerns
If the fish are taken in small numbers (not over fished) and the local waterway is protected from pollution, and the locals are involved and get the money for the fish, then it's fine as far as I'm concerned. If a foreign company goes in and cleans out all the fish from an area and leaves nothing for the local people, then I have issues with that.