I did some quick digging. I found this blurb from dectro that explains why they feel 27 MHz is better.
http://www.aestheticssystems.com/radio-frequency.htm
In it, they claim that 27 MHz is absorbed better. This appear to be true. The dielectric loss factor in biological materials is about twice as high at 27 MHz as it is at 13.56 MHz. This means that for a given current, twice as much heat will be produced in a given time. As I said before, I also think that more current will flow because the capacitance impedance will be less. More current plus more loss factor equals faster heating. I think the idea behind the flash methods is that the coagulation temperature is reached before the nerves figure out the temperature has pulsed up. Hence, less sensation for the subject. Also, faster heating will also localize the heating since the heat flows from high temp to low temp. If you heat slower, a deeper area of tissue will be heated before the layers you care about reach the coagulation temp.
So i think I understand the argument. Of course the only thing that matters is the experience with actual use. If all this is true and works as claimed, one wonders why all the epilators have not switched to 27.12 MHz since this is a standard ISM band and available to all equipment makers.
It seems that 27.12 MHz is commonly used in other forms of medical diathermy machines.