The Vibro-King and the Hot Plate
I can definitely tell the difference in speaker behavior as the power is attenuated. There's also the Fletcher-Munson effect, where you need more highs and lows at lower volumes for the same perception - this is at least partially compensated by the boost switches on the Hot Plate.
To my ear, Hot Plates have always sounded best on the lower attenuation settings. They excel at letting you push an amp into its sweet spot without overwhelming the other instruments in the stage mix. Try to dial the Hot Plate down to conversational levels, and the amp just doesn't sound the same.
The VK has an unusual preamp architecture for a Fender. You can turn the tone controls way down and the volume way up and get preamp distortion at quiet volumes. Of course, this setting sounds like preamp distortion, and doesn't have anywhere near the complexity that the amp normally has when everything's working.
With the Hot Plate, I can use normal tone and volume settings and get all of the amp stages contributing, knock 12 dB off the volume and still keep most of the tone. I lose a lot of the speaker distortion, but it still sounds better that way than with no Hot Plate and the preamp-distortion setting. At 12 dB of attenuation, the room SPL hovers around 95-100 dB, which is way above conversational level, but less invasive to the rest of the household.
I've taken the attenuation to 16 dB or more, and the amp loses a lot of its feel. Changes in tone settings will improve the tonal balance, but can't restore the feel.