What determines whether a 100 watt lightbulb costs more to use than a
1500 watt hair dryer?

Usage time - length of time you use the lightbulb or hair dryer.

Electricity is usually billed in terms of kWH (Kilo Watt Hours), or Watt-hours
if you like. This means that it would cost the same to use your 1500W hair dryer
for 1 hour, as it would cost to use the 100W lightbulb for 15 hours.

Thus, the "Watt" rating, mutiplied by usage time determines the cost of usage:
Cost = (Power)x(Time)x(What your electricity company charges you per Watt-hour)

If you have a "Time Of Use" electric meter (TOU), this could change
the cost.  Since you pay a less amount per kwh after and before prime
time.  If the hair dryer was used during prim time and the light was
used during off peak the light would be less costly

Baldness and / or blindness.

Some electric company also add a base fee for just using there
services so the equation would be :
Cost = ((Power)x(Time)x(What your electricity company charges you per
Watt-hour)) + (base fee)

If the 1500 watts hair dryer is used for time "T" then the cost for
using
the hair dryer is equal to using the 100 watts bulb for 15 * T (15
multiplied by time T). This is because the electricity consumed is
measured
in power units (i.e. watts). Since both the units have been measured in
power units i.e. watts the only determining factor that will cost the 100
watt bulb more than the 1500 watt hair dryer is TIME.