There`s only one phase amplified, otherwise you would simply have two outputs.
The common mode rejection is a very important quality factor of a balanced stage. It directly shows the amount of cancellation common mode signals resp. amplifying explicitly differential signals and depends amongst others on the amplification factor of both signals (and logically, the higher the amplification, the better the rejection).
Furthermore, it`s the cathode resistor, which compensates the two antiphase-currents, so that in this resistor, ideally only DC flows (the higher this resistor, the more precise both signals are resp. the better the common mode rejection is. Best is a current source).
I was too fast with my previous reply, and digged a bit deeper into the subject:
The negative input is of course in antiphase with the signal at the cathode. So with the lampizator circuit you will have some kind of feedforward compensation, due to the fraction of the antiphase input signal, which is coupled into the cathode via a voltage divider. I`m not even sure about the distortion reduction: did some spice sims, which showed more than double the distortion, than with only one input signal. But mostly 2nd-order, which could have a positive influence on the sound.
The lampizator circuit cann`t be something else than a single-ended stage with the fraction of an antiphase signal connected to the cathode
- possibly without any further advantage.
Please correct me, if I`m wrong...