The why rather than the how:
1) instantaneous power as it relates to distortion. In a very short increment of time, tubes can put out a lot more power than transistors or FETs for a given distortion level. This has mainly to do with electron mobility being a zillion times higher in a vacuum than in doped silicon, not to mention asymmetrical drift velocity issues in silicon. But I'll digress here. This is why 'soft clipping' is possible.
2) overload recovery of tubes is much better than solid-state. This is a follow-on to #1. After a transient, there is no reactive impedance to charge recovery in a vacuum like there is in semiconductors. This prevents frequency domain disruptions in tubes (the messing up of harmonics). This is the main point Lavardin has tried to resolve with their own solid-state devices.
There are other more-minor factors mired in the nitty gritty of device physics but these two are the most important, as I see it.
When it comes to steady-state signals, the power levels ARE the same if the Watts are the same. But music is most definitely NOT a steady-state signal. Nearly all measurements and graphs you will see on the performance of an amplifier are based on steady-state. These cannot be used to accurately explain transient phenomena. They can give an overall indication of performance ability, but nothing more. This is why many people believe measurements do not describe how a component actually sounds.
Getting back to the post, efficiency is a separate issue from power output. For Forests, a 50 or 60W tube amp will be great. We had a 55W Cayin on a pair for a long time and it was wonderful. Their impedance is high so they do not demand lots of current, making tube amps the way to go with Forests IMO.
Arthur