So does balanced sound better than unbalanced?
It must do, if it looks better it surely must sound better
I will be interested to hear a more sensible answer though.
I would also like to know more about these cables, NP - particularly those on your LCDs, and how they compare to Audeze's stock
I just want to state before I go any further that I don't believe expensive cables make any audible difference to the sound profile of a headphone (copper making things sound 'warmer' or silver making things sound 'brighter'...). As long as you are getting a signal from your source to your headphone without any unwanted noise and it isn't of some stupidly high impedance then it's all good.
So does balanced sound better than unbalanced?
Hmm, I have to say I'm not sure (crappy answer I know). I agree with what both rids57 and TwsT have said in regards to the objective performance of balanced vs unbalanced signals in that it's largely useless for a headphone out. The practical benefits would be inaudible for the most part. The only real noticeable difference would be that the balanced output would sound louder due to having twice the voltage swing compared to a unbalanced output.
So then it just sounds the same but louder?
Not quite. What I've found is that the internal circuits for amplifiers that have both unbalanced and balanced outputs tend to use rather different designs depending on what output is being driven (note that this isn't always the case and there are some designs which just give a balanced output for the sake of having a balanced out).
My BMC PureDAC is a pretty good example of this. They have actually said that their unbalanced implementation is not that great and that if you are wanting to drive headphones, use the balanced out. If you look at the specs, the unbalanced output has an impedance of around 100 Ohms (lol) as well as built in crossfeed which you cannot turn off (again, lol).
Now you could kind of chalk this up to poor/lazy circuit design (I have the feeling it may have been gimped on purpose since BMC are now releasing the UltraDAC which has 'magically fixed' those issues with the unbalanced out...). Nevertheless, there is quite the noticeable difference in the output sound signature when switching between the two different outputs (think muddy/uncontrolled bass and all the oddities of crossfeed on the unbalanced out versus a fairly clean/unmolested sound from the balanced out).
The above is perhaps a bit of an exaggerated difference but I hope it does serve to illustrate that whether a balanced or unbalanced output sounds different/better is largely down to the circuit design of your source gear. The Auralic Taurus for instance does sound slightly different when running balanced (a more 'neutral' sound) compared to the unbalanced out (seems a bit more lush/thick sounding in the lower mids), but the difference isn't huge.
So,
TLDR: Balanced cables don't really do jack, but amplifier design does certainly make a difference to the output sound.
As a side note, I will say that running balanced interconnects between my DAC and amp have definitely helped to eliminate some of the unwanted noise (probably still a ground loop issue somewhere in my system) in my source chain. The noise floor is pretty much dead silent when running a fully balanced system whereas you can hear a very slight hiss when running just dual RCA's.
Sorry if the above is poorly written, I've just got back from dinner and I may have had a few too many.