It's more about the amps ability to use power to to tap into the hp and give it what it needs to sound it's best.
There are a couple of good examples here. The lyr is one. It does power with refinement. But it never overpowers on hp's that it is rated for. The hd650 has good scale and the lyr taps into what it takes to sound really really nice. There are dynamics brought out by the lyr that I have not experienced with other amps, but it can also bring out delicate abilities that wow me also.
I have never, I repeat never, heard what the he-4 really sounds like until the day that I plugged it into the Pioneer sx1280. It was shocking. The bass "came alive" with weight and texture and just amazed me. Many of these old receivers use the same output stage for the hp out as they do for speakers...no need for speakers taps to get a sense of what they can do.
First, thanks for your attempt to quantify your findings.
Second, am still mystified by terms like "tap into" ??
like the headphones mysteryiously asks for nano-seconds of increased voltages?
the amp somehow knows to deliver "more mW power" despite the volume knob?
there must be some other (electrical?) element I am missing here....