Summary: Is an ultrasonic vaporizer more efficient than one that
just boils water?

It's 20% humidity inside.
I broke out the trusty ultrasonic humidifier.
It's gonna take a long time to get the humidity up.

That got me to thinking...
If the heat of vaporization is the same, why don't I just boil
some water on the stove and get it done more quickly?

Simplifying assumptions to quell the nitpicking:
It's winter, and any heat produced is offset by the HVAC
throttling back.
Assume same energy source for HVAC and humidifier.
Assume the steam generation is well insulated to minimize
losses not related to producing steam.
Remember that the ultrasonic vaporizer cools the mist upon
evaporation and that heat must be replaced by the HVAC.

Looks like both methods will take about the same energy
per unit volume of water.

What's wrong with this thinking?