a good quality amplifier does only one thing: make the signal stronger. that's all.
The design of the amp has a lot to do with how it accomplishes the stronger signal, and what portion of the signal.
A class A amp, amplifies the entire sign wave, and is also the least efficient design.. a class AB amp only amplifies a portion of the sign wave which makes it more efficient than a class A amp, it is also less expensive to manufacture a class AB amp with the same power rating as a comparable class A amp. The Emotiva amp is a AB amp, the Odessey is a A/AB amp, and i could not find out the design of the Anthem, but i would guess is is a AB or some combination design... if the Odessey was operating in class A then that would possibly explain why it sounded the best and had the most dynamics. The Odessey most likely operates in the class A region for the first given % of the power, as you draw more power from it, it then switches to an AB operation, if you guys did not turn the volume up insanely loud the Odessey was probably operating in the class A region during your "testing" which was amplifying the entire sign wave, not a portion of it like the Emotiva is doing and possibly the Anthem as well... If you played all of the amps a higher volume, when all amps would be operating as an AB amplifier then i would guess there would be no discernable difference between them at that point.