Why is power when discharging larger than power when charging a capacitor?
It is not always larger. In the specific case of the demo with the exploding wire, it was larger: the capacitor charged up over a long period (the time constant for large was long), so energy per time was small. When the capacitor discharged ( of the wire was small), power was large because the same energy was dissipated in a very short time. You could imagine the opposite situation: a capacitor charging through a small resistor quickly, and discharging slowly through a large resistor.
