Both of these valves are used to control the flow of liquids and gases but do this differently. 

A butterfly valve uses a flat disc to control the flow. This disc is either at right angles to the pipeline to stop the flow, or parallel with the pipeline in the centre to open the flow. This means that when it is in the open position, the butterfly is still in the flow which can cause a pressure drop, and means it is not as suitable for highly viscous products or products with solids in the line. Butterfly valves are more readily available for over 4” sizing than ball valves and are best used to control the flow of water or liquid products. 

A ball valve uses a ball with a hole in it to control the flow. Turning the valve either opens, partially opens or blocks the flow in the pipeline. When a ball valve is in the open position there’s no obstruction through the middle and the flow can go straight through so it is known as a full port valve. However, this means at large sizes the ball becomes quite heavy and makes larger sizes uneconomical. If you need a full port valve at large sizes, it’s best to look at some form of gate valve.