The advantage of a covered dish is that it is much more difficult for the bird to soil the food or water in the dish. This is especially useful if, like myself, you cannot change the food and water every day. The final questions are what materials should the dish be made from, how should it be fastened to the cage, and how should it be cleaned. Most dishes available today are made from some sort of plastic. This is fine provided your birds are not capable of cracking or breaking the plasticwith their beaks.
Plastic is also fairly easy to clean, although it sometimes takes a long time to dry.
For larger parrots, aluminum or stainless steel cups are designed to be impossible for the very strong and large beaks of the hyacinth macaw to get through. Also available are dishes made from glazed porcelain. These have the advantages of being difficult to break by chewing, and being easy to clean, and they often look better than plastic or metal. They have the disadvantage of cracking easily and must be bought with regard to the amount of lead in the glaze. Only one company, Fenix, guarantees that the level of lead in the glaze meets all federal and state standards at less than .003 parts per million.