Differential Balanced Sound Quality


I've read where running a true balanced (differential) amplifier as such sounds much better than running it single ended (I'm assuming the same amp has both balanced and single ended inputs here).

Why would that be the case? Is it merely the improved SN ratio, etc. from being balanced, or is it something circuit related with running each channel's plus and minus through separate amplification stages?
greg7
@atmasphere - Ralph - another excellent explanation. Thanks. 

I've been a big fan of balanced circuitry and cables since I discovered what a difference they could make in my system in the late 80s. Never looked back.
Also, I took the opportunity to read the article I linked. It has lots of good information about the 2nd harmonic, but none about the 3rd. Here’s some more Pass writing that discusses both:

https://www.passdiy.com/project/articles/audio-distortion-and-feedback

And here in the introduction (on p3): https://www.firstwatt.com/pdf/art_ba_3.pdf
I'm just a newbie compared to most here if not all. I recently converted to what I believe are true AES48 supported pre-amp and amp (wyred4sound both units) and can say that the noise floor and transparency have never been greater in any system of mine in 30 years. The noise floor is basically inaudible. I am currently using "simple" balanced cables with Neutrik ends and mogami wire between the gear and quite happy. I have other weak links in the system but this is not one of them.  

Thanks to the knowledge freely shared here. 
Here is a quote from the late Charlie Hansen in The Stereophile, talking about their Ayre Codex, their cheapest electronic component having a linear power supply: "remember that every circuit is a modulated power supply....When you run balanced, it is like making the best power supply 1,000 times better."

@oldears Great quote.  There's someone over on diyaudio who's posting tag is "The power supply of my power supply is my FRIEND!"