Answer
Less damage is done by plugging a 220-V hairdryer into a 110-volt supply outlet.
Work Step by Step
Damage is done when too much current is driven through the appliance.
In a hairdryer, the resistance of the heating element is tailored to the expected supply voltage.
Plugging a 110-V hairdryer into a 220-volt supply outlet will cause twice as much current to flow as the hairdryer is expected to handle. On the other hand, plugging a 220-V hairdryer into a 110-volt supply outlet means that only half as much current flows as normal, and no damage will be done.