Balanced versus single ended

There is also talk of more gain with balanced. As I understand it the extra 6dB is a lower noise floor rather than extra gain.

That’s not correct. The extra 6 dB is the doubling of the signal amplitude due to having 2 signal wires with opposite polarity. Here’s an online calculator. Put in 1V as the start, 2 V at the end and it will come out to 6. This is the same ratio you get when going from RCA to XLR.

https://aetechron.com/calculator-Volt2dB.shtml

As others have noted, with short runs away from noise sources the noise is the same.

So, in terms of the signal to noise ratio (S/N) the N isn’t reduced, but the S is increased.

I can only say my present setup, balanced from digital source through real balanced pre, finally through monoblock amps, which are also in effect, true full balanced I get best sq.

I've also had any number of se components over the years. Certainly, I have higher resolution than systems or components that contained se. Still, without having the choice on most or present components to directly compare hard to say. Balanced does have advantage of lower noise floor, and components that are truly balanced have inherent advantages as well. Not sharing power supplies, output transformers in case of tube components, signal path circuit is only good.

In case where component is not truly balanced, I can imagine se being better, in this case balanced is add on, using transformer or some other scheme for xlr.

The issue goes beyond simply the use of different cables as the "standard for balanced line operation" that Ralph often discusses focuses on how audio equipment is designed with respect to grounding and shielding as discussed here.

Could there be sonic differences based solely on whether the equipment is designed to be balanced or single-ended, probably, but how that single difference would affect the sound we hear is something I couldn't predict.  If implemented properly, the balanced gear should be have less noise.  However, it has not been my experience that fully balanced equipment is immune to all facets of IC cable design such as wire gauge, geometry, shielding, connectors, and materials,  but then IME most cable changes are subtle not revelatory, so YMMV.

Certainly, long runs, if equipment offers, use XLR to protect from the added potential of problem(s). But, even a long run at home, really not the same need as a swarm of this and that in commercial setups.

Short runs, home audio system, why?

One clear advantage is the snap in locking connector. 

For stable matched secure contacts for L and R, I changed all my interconnects to locking rca connectors, and use XLR/RCA from my Sony CD player's XLR out, just to compare. I cannot hear any difference between it's XLR out or it's RCA out.

I don't really have a strong opinion in an otherwise well functioning home whether you go with XLR or RCA, but I will say that if you build your own, Neutrik has silver contact XLR's and Parts Connexion has a line of pure silver, balanced IC cables you can combine to make outstanding / end game interconnects for a lot cheaper than you'd buy.