Thanks for the answer jaddie. I think with certain headphones (e.g. HE-6) balanced output does have a benefit since it has a lot more power output. SE output of 2W may not be enough to drive the HE-6 but balanced output of 4W is better. but yeah i guess for other types of headphones you can argue that balanced has no noticeable effect.
Balancing doubles the output voltage, which would, in theory, quadruple the available output power. But there are other factors, such as the circuit's current capability, power supply, etc, that may limit that to somewhat less than the expected quadrupling. You could, however, get the same improvement by just doubling the SE output voltage. Headphones don't "know" or "care" how the voltage is delivered, the drivers just respond to a voltage across them.
Just because you have an amp with higher output power doesn't mean it will improve anything unless you actually use that power. So the HE-6 with 4 watts is an advantage for certain headphones, because they require that power, but others do not. You can increase the output power capability infinitely, but what matters is what the load uses. Consider a 15A electrical circuit in your home can deliver up to 1800 watts. The average light bulb consumes 40 watts. Changing to a 20A circuit increases the capability to 2400 watts, but the lightbulb still only consumes 40.
but still, since balanced output is the signal and its opposite phase, ans SE is just the signal and ground, shouldn't balanced out always be double SE, in terms of power? given that they are using the same balanced only circuitry that is, not not a separate SE only circuitry with different power output.
Ignoring current source limits, doubling the output voltage will increase the available output power 4X. Just inverting a SE output with an identical but inverting amplifier doesn't guarantee 4X power, though.
As to balancing always doubling output voltage, it depends on how the balancing is achieved. If you start with a SE output, then go through an inverting, unity-gain amplifier, the difference between the SE output and the inverted version will be twice the SE voltage, and differential. However, if you run that SE output into a 1:1 transformer, the output will be balanced, but the same voltage as the SE output. Analog Devices makes (or made) a "balanced line driver" IC in two versions, one was not gain corrected, so you got the +6dB/voltage doubling, the other was compensated so there was no voltage increase. There are also active balanced output circuits that if connected as a SE output by grounding the unused output, they increase their gain by 6dB to compensate, such that balanced or unbalanced, the output voltage is the same.