Is it really the Power required for comparing input and output?
The power output for any voltage regulator cannot exceed the power input. That's a fundamental rule of nature.

In the real world, the power out is less than the power in. The ratio of power out to power in is the efficiency of the regulator.

A switching regulator can have a higher output current if the output voltage is less than the input voltage, or can have a higher output voltage if the output current is less than the input current. However, a linear voltage regulator must have a higher input voltage than its output voltage and a higher input current than its output current. That means that the efficiency of a linear regulator is usually much lower than a switching regulator.