What are the major advantages of using a closed-loop over an open-loop and vice versa?
If you understood what those terms meant you wouldn't be asking this, so I'll explain open loop and closed loop.

Open loop means you pick the set point of a system and whatever comes out comes out.  No system is perfectly "stiff", so the output will vary somewhat, sometimes quite a lot, depending on load.

Closed loop is when something is actively watching the output and adjusting the set point to whatever it takes to get the desired output.

Think of the gas pedal in your car.  From gas pedal to car speed is a open loop system.  You can push the pedal down to a fixed spot, and the car will go faster or slower depending on whether it's going up a hill or not and what else it has recently done.  Now consider cruise control.  That's puts feedback around the open loop gas pedal to car speed system to regulate the speed.  It watches the speed and effectively steps harder on the gas when it notices the car slowing down, and lets up on the gas when it goes faster than desired.

The advantage of a closed loop system should now be obvious.  You get to control the parameter you really want to control (the car speed in this example), and it automatically gives the system the right input (the gas pedal setting) to achieve the desired result.  Of course this comes at the cost of extra stuff and complexity.

Closed loop control systems also need to be designed carefully so that they are stable.  For example, if the cruise control always slammed the gas pedal to the max whenever the car was a little below the set speed, and completely let up when a little above, you'd have a very jerky ride and it would put a lot of stress on various parts of the car.  Usually there are some tradeoffs the designer can make between the maximum error, the speed of response to changing conditions, and stability.