LEDs are more efficient because of their efficiency to convert electrical energy into light energy. Which is simply due to the semiconductor technology, not the drivers. Drivers actaully reduce the efficiency of LEDs due to energy losses from the transformer and rectifyer.
Assessing LEDs by power draw is actually an acceptable way to see how well it performs, though the best method is with integrating spheres. This is a highly complex and unpractical method however. LED products that are fairly cheap and low cost, typically have efficiency levels less than gas discharge, which is why using the total power consumption is good rule of thumb. Remember, even the energy losses from the drivers and other connected devices, are combined in the calculation of electrical efficiency, you cannot ignore them.
The best value light technology is gas discharge, commercial horticulture companies know this and is the main reason why most commercial indoor facilities are still gas discharge. LED technology is still some time away from being able to regenerate investments over rational timeframes. LED products such as california lightworks, spectrum king, fluence, nextlight, and black dog that provide comparable performance to sodium discharge, require a substantial investment that take years to recover the initial costs.
Evetually LED will superseed all lighting solutions but that time is still a few years or more away. I will myself, knowing lighting technology and plant science. Will continue using gas discharge, until LED has reached a stage of practical and economical value.