If properly used, copper, teflon, or ceramic dishes will ensure quality of cooked foods. However, here are a few benefits of copper dishes
Copper allows cookware to heat evenly. This helps to prevent hot spots on pots or pans, and for foods to cook more evenly. Evenly distributed heat during cooking prevents undercooked interior in foods.
The weight. Copper pots or pans sit well on the stove, while being light enough to be lifted when completely filled with food or water. This increases flexibility during cooking.
Copper is a good heat conductor. When the stove top temperature is changed during cooking, temperature of the cookware changes rapidly. This is beneficial for some cooking methods, such as browning foods.
Some people have too high copper levels, and should not use copper pans. This includes some schizophrenics. Teflon may flake off into the food, and fluorine is not an element I want in my food. I suggest using ceramic.