Page 6 and 7 of the blockhead manual explains some advantages of balanced driven headphones.
Balanced differential drive also gives twice the slew rate and twice the voltage swing. The faster slew rate keeps up with and provides faster, more accurate, and precise audio.
The higher voltage swing means louder volume, so to listen at the same volume as unbalanced, the gain has to be lowered or the volume turned down. Once the volume level is down to the same as unbalanced, the voltage swing is the same. The advantage of having two amplifiers on each earpiece is twice the current capacity which is mainly needed for really powerful bass that is fast, accurate and precise. Thats a real slamming snappy power full bass. The more you turn up the volume, the more noticeable it becomes.
The ground wire is not used at the headphone but is used at the amplifier to reference the audio signals to each other and evenly between the power rails. The DC offsets are also driven to the same zero volts ground reference to keep the headphones from having any DC voltage which could damage them.