Just got a new power amp

Thought the conscience was to always use XLR, they have a much lower noise floor, carry less noise, have less signal loss, of course higher gain. 

Why would you not? Lowering the noise floor is always an improvement.  

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.