Balanced versus single ended

Balanced will always sound louder, but your system isn’t going to be capable of playing louder. So you have to adjust the volumes to be the same for a true comparison of quality.. Fortunately my Audio Research equipment allows that. So I can flip between them with the volume equalized.
 

The only direct comparisons I have done was with Transparent cables and Audio Research gear (all balance designs). I was not able the discern a difference. 
 

I think in most cases it is negligible or at most a small difference. If the component design is balanced and you use single ended interconnects… then inside the components are converters to change from balanced to single ended and visa versa.  In high end equipment, the designer puts effort and high quality sub components into doing it. 
 

XLR cables cost more… often a lot more. If I was relatively young I would go with balanced… component design is headed that way. But if I was on a budget you can save money on single ended. But as has been pointed out to be sure with your components, you have to try to be sure.

As with most things the devil is in the detail, I have heard both in many different guises and believe that, on its own neither makes an audible improvement, its far more about how the technology is put into practice.

A fully compliant AES 48 installation with good cables will always measure better than a non-balanced RCA installation. Regardless of line-length, noise rejection and other cable artefacts and earth separation will be better. In theory, it should sound better - in my experience it does.

Ahh another draw ! If Your system was completely dual..balanced and not, A/B testing could be done with equal length and quality cables. Perhaps then theory and measurement would have ironclad credibility. Kind of a moot point as few system components will be wired that way. So you have a system with XLR, RCA, mixed Components maybe servo control, if it’s fabulous who cares. 

Balanced is theoretically better than SE.  Separating the ground between the 2 channels eliminates a lot of hum and crosstalk-type issues.  This doesn't mean that it will always sound better to all listeners, but it shouldn't sound worse unless there's an implementation issue.

You're never "required" to use an op amp.  Normally, that would suggest that the design is already op amp-based, or that they're using it to invert the signal at some stage to create a balanced signal.  A discrete gain stage or op amp is required to convert any SE inputs to balanced operation.  In the case of Audionet, they appear to have developed a proprietary op amp that is presumably used in all their active stages.