The assumption here is that the B+ connection has the same signal content and impedance as the ground. The input signal is given to the grid while the cathode is loaded by a resistor that leads to ground or a negative power supply.
The gain is always less than unity, the output impedance is roughly the reciprocal of the transconductance, and the PSRR is roughly equal to the inverse of the mu.
An intrinsic distortion correcting mechanism known as degenerative feedback keeps the Cathode Follower's distortion low. It works this way: any departure from the desired output voltage will subtract from the input voltage and result in a countervailing change in current flow. In other words, if the cathode is forced more positive, the grid will effectively become more negative relative to it and thus less current will flow through it, which works to decrease the output voltage; on the other hand, if the cathode is forced less positive, the grid will effectively become more positive relative to it and thus more current will flow through it, which works to increase the output voltage.
In other words, the Cathode Follower relies on the tube's transconductance to keep its output voltage in line with the input voltage. Thus, the greater the transconductance, the lower the output impedance.
Unfortunately, in spite of low distortion, a cathode follower can sound bad if sloppily designed or improperly used.
One advantage a Grounded Cathode amplifier has over the Cathode Follower is that the plate resistor and the cathode resistor (if it is not capacitor bypassed) both lower the transconductance of the triode. This would seem to constitute a disadvantage, but a high transconductance that is not matched to a high current draw, in my opinion, worsens the sound. I like to use as much current as there is transconductance, which is not possible with