Why the water in copper Pot is cool
Clay jugs just have the property to keep water cool. They used to act as water coolers of the by gone era, they can reduce the water temperature by a few degrees lower than the room temp. Since the clay jug is slightly porous some water passes though its body and evaporates .As the process of evaporation occurs it takes away some heat from the contents of this jug thus causing cooling. Don't try this by the way. Most us are not used to drinking this water and lack the resistance that our elders you might get a sore throat ( I know from experience I used to try all these experiments when I was young). its possible that in the clay jug overnight some microbes might breed, which could cause a minor throat infection.
Stainless steel and glass jugs are now used cause they are cheap and modern alternatives to the no longer required copper,silver and clay jugs. we now have water coolers/fridge and aqua-guard
TO FINALLY ANS YOUR QUESTION : it really makes no difference from which jug you drink your water as long as its clean drinking water that has been filtered.