I *suspect* that a really hard regulated amp with no headroom would perform more ideally up to clipping. More like the voltage amplifier it should be. Of course this could depend on all kinds of factors! Nevertheless I feel this might be why some high powered built-like-a-tank amps are felt to have "more control" even when not played up near clipping. Needs more research...which will never happen...
Amplifiers can behave perfectly well up to, and into clipping and others can momentarily latch up, oscillate, or otherwise lose control. The modern Class Ds are excellent at the onset of clipping in the limited tests I have done. I have plenty of older amplifiers that can do some crazy stuff as the NFB loop loses control.
The thing is, as the current being delivered by the amplifier increases as you push more power, the devices in a typical Class AB drop more and more voltage across their junctions, emitter resistors and, at the same time, the main rails sag as well. So you have these dynamic modulations of the supply rails resulting in non-linearities that the amplifier vainly tries to correct via feedback. Most high performance designs will run the front end (differential stage, current mirror/s, VAS etc) from a separate and regulated higher voltage supply, so the actions of the output stage (the current amplification part) do not affect it so much.
But a huge number of typical class ABs, just attempt to decouple the front end supply rails, via a resistor or two and some caps, which can also mean the front end voltage is incapable of driving the output stage to its full potential.
The FETs used in Class Ds already have a phenomenally low Rds(on) (resistance source-drain) which means the losses due to drops over the device are much lower. Combine that with super fast switching with little time between off and saturation and you have fantastically low losses.
Taking amplifiers right up to the edge of clipping under load and watching their behaviour live on a 'scope is most illuminating. All amplifiers are not created equal and they certainly don't perform the same or sound the same in that situation.