Choosing the replacement bulb only by their wattage is no longer a easy task like in the old times when the incandescent bulbs were the only option, and everyone understood the bulb brightness by wattages like 60 watt, 80 watt or 100 watt.
The WATTS is a measure of the amount of energy used by bulbs and the LUMENS is the measure of brightness provided by a light bulb (more lumens, the brighter the bulb is)
Starting with energy efficient bulbs coming along in the market, the most crucial step in understanding the amount of light generated by the energy saving light bulbs like CFL Bulbs and LED is to understand the Lumens
Beginning with 2012 FTC required for the light bulbs labels to Emphasize on Lumens, Not Watts, as a Measure of Bulb Brightness
In general a simple rule to replace an incandescent with an equivalent in light output CFL bulb is to select the CFL bulb that have 1/4 watts compared with the replaced incandescent bulb. So for example if you are looking for replacing a 60w incandescent bulb than the right CFL bulb will need to be a 15 watt bulb.
While the math for the CFL bulbs is simple, the LED bulbs are even more energy-efficient and more durable than compact fluorescent light bulb. LED requires less wattage than CFL for the same amount of light.
On the left side is the comparison table for the most common light bulbs used in the households, useful in selecting the right replacement lamp for your application.