When talking about balanced, it's best to refer to it as a balanced SYSTEM and not reduce it to just a cable.
Most balanced amps are going to be better in quality of build as it's most manufacturer's flagship product compared to their run of the mill single entry stuff so it's not going to be comparable regardless. Most of the time a brand's balanced output rig is going to sound generally better. Whether or not the topology has any merit is still left to you guys buying the stuff, but it's really comparing apples to oranges. As a consumer it's natural to suspect that all this crap is pretty useless and they're going to need to really sell us on it, but some of the people building amps REALLY do know what they're doing.. just as long as you know who it is haha.
Headroom invented it, and more or less has run with it since then and many other manufacturers are doing it now. I'm not sure where their amps stand now, but when I started in the hobby they were tops in the game and we were fuelling some pretty thirsty cans back in the day too.
The "benefit" of running balanced is yes, separating the two channels, It's not just the cable, but by as much as possible starting from the source onwards to the cans. Usually a balanced amp will be basically double the amp so you're getting more power naturally going to each channel. Is it better than single ended? Honestly I still have yet to have an idea resembling that. I just know that cables are expensive and not everybody is down to buy a $1000 superamp, but it's probably one of the last things you should worry about while shopping for gear. Just buy whatever you can comfortably afford as long as it comes from good people who've been in the business for a while, and worry about graphs and nomenclature later. A hungry audiophile is an unhappy one :)