Tesla coils, either classic (with spark gaps) or electronic (with transistors) are impulsive devices. Measuring and comparing power is much more complicated than it initially appears.
With a small electronic coil, the peak current to the primary of the tesla coil can be up to 1MW. This sounds huge, especially for a device that is sitting on your table top and is not engulfed in flames.
But, the answer is simple, the 1MW is only drawn for a very short time and each pulse grows exponentially to this maximum, it isnt constant. In the terms of a small table top electronic coil, the power pulse can last for 100-150uS (1/10000th of a second) and is repeated maybe 500 times per second, during each pulse the current grows exponentially so this gives an average power of roughly 4KW (1Khz – 100uS)
I couldn’t run the coil like this for long without overheating so I allow this for very short periods of time, or if the on time is known to be longer I will limit the output of the coil to that which is sustainable.
As you can see from this, doubling the frequency doubles the power. This explains why the lower frequencies have smaller sparks.
It also explains why I like ‘plonky’ percussive electronic music playing on my tesla coils.