It's not really that simple. Real balanced, aka 'dual differential' requires exactly mirror-imaged circuits, one for the pos side of the music signal, the other for neg. IN single-ended, ground is referenced and hot changes from + to - as the sine wave goes "up and down". getting balanced to be totally-perfect exact mirror-image is quite difficult, and takes twice the number of parts, and more real-estate, which also opens up the possibility of more "parasitics", aka side-effects. So, "balanced" is not automatically better - unl;ess it is properly implemented.
As far as power goes, it's not just about "volume". There are lots of "power" specs that tell less than one would think. Flashlights quote hgh lumen numbers, but that is not always how much light intensity actually comes "out of" the flashlight. Measuring horsepower of a car engine, not actually "ceonnected" to a car is another- gear ratios, weight of the car, aerodynamics etc also play a role in 'how fast' the car can go.
Speakers/headphones/iems are almost always reactive loads, and have back emf (i.e., they are moving targets, and they fight back-- it's like the difference between sitting on a tame horse used for "kiddy rides led by a handler holding the reigns and walking along side, vs a rodeo bucking bronco. So, more power contribnutes to the effortlessness of the sound, espcially if the amp is well designed, does not have its global feedback messed-with by the load's back emf, and can keep the load under control thru various impedance swings, etc... Many manufacturers of portable dacs/daps/amps quote maximum power under quite optimistic circumstances, so some raw numbers do not tell as much as some folks think they do.
Lastly, the quality of an electrical connection is a function of (among other things) contact area and contact pressure - 4.4s are instrinsically better than smaller connectors, So it's not just the 'balanced' part of the situation either.....