Well if it sounds perceptively better then it would most likely be due to reduced noise floor, ground loops etc. Technically given the same set of electronics, it really should not sound different. If it does then I would recommend further investigation - either you did not match volume levels precisely when doing A versus B or you may have a problem with your equipment, cables or both. Certainly worth investigating as you should not be hearing differences in a situation where everything is working correctly.
It might be sound level although when I did the A/B test with the BHA-1, I changed the gain switch to more accurately match the sound level between the two cables.
I should say that with most music I don't hear a difference but with classical music I've listened to for more than 30 years, I just seem to enjoy it more when listening to it with a balanced cable. Cables are Cardas Clear and the BDA-2 is being fed from my BCD-1 with a Cardas Lightning 15 digital cable. When using the BDP-2 as a source, the connection to the DAC is Cardas new Clear AES cable.
The connection to the Sennheiser HD-800 is Cardas new balanced headphone cable.
Again, it may be the extra gain of the balanced input is making the difference but I don't just flip back and forth, I listen for long periods before switching.
So for now, I'll buy the idea that there shouldn't be a difference in sound if the comparison is an apples to apples comparison. I've just ordered more new Audio CD's so I'll stop worrying about hardware and try to enjoy the music.
Bud