What is the difference between open and closed screw banana plugs?

The Open Screw type has the benefit of being a little more versatile. The side entry option means it can accommodate thicker gauges of wire or bundles of more than one conduit. It can also piggy back other connectors while terminating bare wire at the same time. The Closed Screw type has the benefit of providing a cleaner finish. Because there is no hole in the side, there are no exposed strands of wires. This also reduces the changes of shorting across terminals.