I have been thinking about this issue for awhile. One must remember that "balanced" headphones are not truely "balanced" The 3 pin XLR jack provides a true balanced connection on the back of audio equipment. It carries 3 wires, a ground, a positive, and a negative (this negative is the same amount negative as the positive is positive). These 3 wires are for one channel, with another 3 wires for the other channel. The :"balanced" connection has been used mostly by the "pro-audio" community for years, and is favored over single ended connections for thinks like microphones and guitar pickups where a low signal is carried for a long distance, often in an area with many competing signals. They also use the TRS connectors. (think guitar jack). The 3 pin XLR jack is a popular "balanced" connector, and is still used if you have "balanced" source devices. Of interest, one does not need "balanced" source for there to be "balanced" output from your amp. The output transformer can output balanced signal from a single ended input.
"Balanced" headphones however, refer to each headphone element having both a ground and a signal wire to it. A total of 4 wires for a set of headphones. There are no third wire connection that would be a proper "balanced" connection. I think a pair of XLR plugs was used because it is a proper "balanced" connector, and since there are only 3 pins, then 2 were needed.
Simply hooking two 3 pin XLR plugs onto an amp with a common ground between the 2 channels is functionally the same as a single ended connection. A true "balanced" amp will have the signal ground separated from input to output, and I think that is why there is improvement, not the fact that there are 2 signal wires, and 2 ground wires going to the headphones.
All that being said, my balanced headphones have dual XLR connectors, and they are heavy, and a lot of real estate is used on the amp for the connections. I would be in favor of the 4 pin XLR as a new standard, although I would not be switching any time soon due to my current gear.