disadvantage i can mention right now is parasites.
It depends on the importer when it comes to diseases/parasites.
All that I've bought from are given antibiotics and antiparasite treatments prior to being offered for sale (and held 2+ weeks after treatment is over).
I've NEVER had a parasite/disease issue with wild-caught fish except for an order of Otocinclus cocama (Zebra otos) that arrived in the bag with ich. Out of a batch of 10, two died within 24 hours (and refunded by the shipper). That was the first time I'd ordered from an out-of-the-country supplier, but I could not find them in the USA anywhere for sale for over 8 months of looking.
I've had plenty of parasites/diseases brought in from a LFS with mass produced fish like guppies, mollies, platies, neon tetras, various danio etc.
another one would be getting the wild fish used to regular flake and pellet food or food that doesnt move. once youre past that you have won more than half the battle with wild caught fish.
Amen to this disadvantage with some fish! I have one species that after the 3rd generation tank-raised, is just starting to take an interest in commercially prepared foods. I don't mind providing live food to my fish (and do for most meals), but it makes them more 'marketable' if they will eat flake/pellet foods.
advantages? i suppose less of a chance to get very inbred individuals, an interesting coloration or pattern only see in wild caught fish perhaps. that depends on the fish.
And usually a much larger variety of fish available than even the largest LFS will have in stock. The wild-caught fish, in my experience, adapt very quickly to captive life if you keep their aquarium clean and more 'natural' for them. If they come from fast moving rivers/streams, provide them with a submerged powerhead for more flow. If they come from heavily planted, slow moving waters, provide that.