It is easier to catch an animal related disease and it is not known if transplanting animal organs can result in outbreaks of animal viruses. It hasn't been very successful in the past. The transplant recipient can suffer from potentially fatal graft. Also it could affect lifespans as pigs, for example have a totally different lifespan to humans and their tissues age at a different rate. An ethical argument would be that animals should not be harmed for human benefits and the disadvantage would be the rise in conflicts and disputes.