Just got a new power amp

@atmasphere 

I'd put it the other way 'round. We audiophiles are very used to hearing interconnect cable differences. But recording engineers, who use balanced lines in a studio, are not. When the balanced line system is set up properly (as usually seen in a studio) the 'sound' of different interconnect cables goes away. 

Agreed.  I was not limiting my "something" to the physical cable.  It could include associated equipment and/or the observer.

One criteria of balanced output is lack of GND return current.

@kijanki So if one side is at ground, but there is no ground return current to any other part of the amp, your criteria is satisfied? Or is the fact that the speaker circuit is not complete without a ground connection a problem?

Audio Research used to ground the 4 Ohm tap of their output transformers rather than the common tap, so they could cathode cross couple the output tubes; IOW the cathodes of one half of the amp were tied to the common tap and the 16 Ohm tap was tied to the other half of the amp's cathodes, as a feedback mechanism. To do this obviously the feedback was balanced. Does this meet your criteria?

@atmasphere   Tube design is your domain so it is not wise for me to argue, but grounding tap of transformer’s secondary won’t make current return to GND.  Transformer output is balanced, but stage driving primary might be not with one transformer tap returning current to GND.  

I’m sure we can find many exotic configurations that could qualify as Fully Balanced, but PS Audio amp, that started all this, is not.  It is single ended class D amp with differential input stage.  Something should differentiate between this and fully balanced design, like one in the schematic I referred to.   To me it is word "Fully" suggesting, all stages are balanced.

@kijanki Right.

(We introduced a class D amp of our own design about 4 years ago FWIW.)

The question then becomes, in the context of this thread 'is it important?' WRT the thread title, it isn't. Ampex made a tape machine that was used for quite a lot of the recordings made in the so called Golden Age of stereo (1958-1963); that machine had a balanced input and output using transformers but the internal electronics was mostly single-ended. Its use of transformers allowed it to be immune to interconnect cable differences.  

@atmasphere  I agree, "Fully Balanced" design doesn't have to be better - net result is what counts.  There are many imprecise popular or marketing terms in use, why to argue.  I noticed that many great companies still use erroneous "watts RMS" and wonder if it is on purpose.  They likely know it should be just watts or watts average, but that is what most customers think of (product of RMS voltage has to be RMS power) - cannot blame them.