Just got a new power amp

If there is an audible difference, something is defective.

@kr4 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. 

Having done many auditions of this difference over the last 40 years I can say that RCAs usually don't sound as good as a result and nothing is defective; this providing that the balanced line equipment actually supports the balanced standards (such as AES48). 

"Fully Balanced Amplifier" means that balanced input section (instrumentation amp or transformer) is followed by two separate amplifiers, each driving one speaker terminal.

@kijanki Could you explain what is meant by 'two separate amplifiers'? Do you mean two single-ended amplifier circuits or two push pull amplifier circuits, or something else?

@atmasphere   "Fully Balanced Amplifier" is in my opinion an amplifier that consists of true balanced input stage, like transformer or instrumentation amp, followed by two amplifiers - each for one leg/phase of the signal.  Speaker is connected between outputs of both amplifiers. 

Icepower 300AS1 module in S300 amplifier has balanced input stage and Mosfet bridge on the output (switching speaker direction), but is not "Fully Balanced", but rather amplifier with balanced input - often called "True Balanced" when done right (no GND reference)

@kijanki Our OTL tube amps are fully balanced and differential. But to the best of my knowledge, there's only one output section (which is push-pull) driving the speakers. Does this meet your definition?

@atmasphere   Fully Balanced, in my opinion, would require two output stages - in your case two Push-Pull stages, which probably wouldn't make much sense.

If we call S300 amplifier "Fully Balanced", then do we call Emotiva XPA-1 "Fully, Fully Balanced"?  

This is design description of Emotiva amp:

"Rather than the two sides of the amp driving two independent channels, the XPA-1 uses the two “channels” of the amp to drive the hot and cold legs of the balanced input signal. The single ended input is copied, and the copy is inverted to feed the two sides of the amp. This is the ultimate expression of balanced drive, with two completely separate halves of the amp used to amplify the inverted and un-inverted legs of the input signal, and then recombined at the output. This completely cancels out any common mode noise that both halves of the input signal see in the amplifier. Bridging a stereo amplifier, as you can do with the XPA-2, does not offer the noise cancellation offered by a fully differential design."

I got this particular amp's name from this article, that talks about challenges of such design:
https://hometheaterhifi.com/technical/technical-reviews/the-fully-balanced-power-amplifier-advantages-and-design-challenges/

IMHO, Fully Balanced configuration (as I call it), doubles the circuitry (cost), with little benefits (other than high output power).  Cancellation of even harmonics is probably not high priority by the most, while small improvement of CMRR is not worth it.  
 

@kijanki Its hard to know what Emotiva is talking about since there appears to be a typo or complete misunderstanding of what is happening in the opening sentence of the quote of the description; power amps do not drive the input, if you see what I'm talking about. A preamp might do that though...

Anyway, IMO/IME your definition is a bit too restrictive. Our OTLs are an example that flies in the face of it and are one of the oldest fully balanced differential amplifier designs in production. 

Fully Balanced configuration (as I call it), doubles the circuitry (cost), with little benefits (other than high output power)

This statement is false if the circuit is also differential. You do have more parts but not double. Depending on the gain of the circuit the CMRR can be quite high. 

There are amps that are fully balanced but not differential. I see no advantage to them at all, since they often offer no CMRR and do indeed have double the parts. 

Apparently Douglas Self doesn't know about our stuff since he makes the claim at the link you provided:

To my knowledge these are the first, high power, full balanced amplifiers with feedback from the input to the speaker terminal in high volume production.

We've been doing exactly that for 40 years although its been with tubes, but he might be right depending on what is meant be 'high volume production'.

Now if you want, you can build a conventional tube amplifier using a differential Voltage amplifier and transformer coupled push-pull output. In fact that is exactly how our little Gem integrated amplifier works (it only makes 5 Watts/channel, meant for headphone, bedroom or desktop use, but you could use it in a main system with high efficiency speakers). 

Depending on how you execute the ground at the output, you could have balanced feedback loops or single-ended. Yet the amp is fully differential and balanced from input to output. 

I really think you need to expand your definition, since as you have stated it so far makes a good deal of your arguments false, for example the bit 

like transformer or instrumentation amp, followed by two amplifiers - each for one leg/phase of the signal.  Speaker is connected between outputs of both amplifiers. 

This statement would only be true if the word 'amplifier' meant only a single-ended circuit. Obviously there's a bit of a contradiction were that the case since the input allows for differential circuits which are not single-ended.

Further, whether the embodiment is tube or solid state is irrelevant.

For example, I'm sure you've heard of GAS, who made the Ampzilla. That amp used an output circuit known as a Circlotron, the same as our OTLs. If that circuit were used with a differential balanced input (like we do), you'd have a fully differential balanced amplifier with only a single amplifier section driving the speaker terminals and it would be up to the designer as to whether a single or balanced feedback network would be used. 

So I really think your definition/opinion has you painted in a corner unnecessarily.