People measure amplifier power in different ways. The only thing that matters is whether, at the desired listening level and into the desired load, the amplifier is able to fill the waveform without distortion. If the load has very low impedance, the amplifier may not be able to provide the necessary current, the voltage will sag, and the waveform will assume a different shape than the incoming signal. If the person turns it up too loud, the amplifier is asked to create voltage levels higher than the rail voltage being switched in by the amplifier devices, and the voltage sags, often abruptly. Both of these fall into my description: clipping.
Clipping is usually audible and must be avoided. If that's what the OP means by "demanding conditions", then the solution is a design that provides more power at the desired listening level and into the desired load so that it doesn't clip. The limitation may be the power supply, but it may also be the active amplification devices and surrounding circuits that become saturated.
If the power at which the desired listening level and load is supported without distortion is the same between two amplifiers, then the cheaper and more efficient design would normally get better engineering marks. They should report the same specifications, but of course they don't, because the standards for reporting power output just pick one condition, not all conditions. When I look at measurements, I ask what the power output is relative to load and frequency, and relative to distortion levels. Even with all the measurements we see these days, it's not always obvious.
The term "dynamic power" or "headroom" means little to me in practice. I suppose it usually means the ability of the amp to fill some rogue waveform at a higher power level than specified within some acceptable distortion, to provide sufficient current at the maximum rail voltage for some useful but not indefinite period of time.
Is the OP is asking for is a power supply that at the rail voltage can supply all the current necessary indefinitely? Regulated switching power supplies are designed to do that, and so don't have "headroom". And they do that without car-sized transformers and garbage-can-size filter caps. Unregulated linear power supplies can always do more for short periods of time. If the maximum continuous output is the same (which is a statement that carries a lot of freight), and if that continuous output is sufficient to achieve the desired listening level into the desire load without distortion, then what does it matter?
Rick "late hit, I'm sure" Denney