6 -- No. I believe you're confusing Power with Gain -- easy to do, but two distinctly different things. In your scenario, both tubes still produce the same amount of power output -- but the tube requiring only 11.75 volts of bias will reach full power output sooner than the tube that requires 13 volts of bias. Now granted, if the input signal is advanced so as to drive the 13 volt tube to full power ouput, the tube requiring only 11.75 volts will now be over-driven. But again, once the tube saturates, maximum power is achieved. In your scenario, one tube is just achieving full power before the other because it is displaying more gain.
Dave -- In a Class A (single ended or push-pull) design, the tube or tubes by definition must conduct current at all times over the entire excursion of the input waveform, from quiescent to maximum power output. For the tubes to produce an equal maximum excursion on either side of the operating point then, while never being driven to the point of cutoff, that point must therefore basically be located in the center of the load line. Such operation requires a heavy quiescent current to be drawn, which therefore requires a reduction in B+ voltage so that the tube's plate dissipation will not be exceeded.
In a Class AB design, the operating point is moved off-center on the load line, and pushed close to but not up to the point of cutoff. Since this greatly reduces the quiescent plate dissipation, it allows the opportunity to raise the B+ to once again cause significant (but not excessive) plate dissipation to occur under quiescent conditions. With an off-center operating point however, it means that the output stage must now operate with two tubes in push-pull, with each tube conducting current during slightly greater than half, but much less than all of the complete input waveform applied to them, in an alternating fashion. This scenario allows for greater dynamic plate current and plate voltage to be developed from each tube (albeit for just a little more than half a cycle, each), and therefore represents a reduced output impedance which in turn, allows for the use of a lower impedance output transformer. A lower impedance output transformer has a reduced turns ratio between the primary and secondary winding (i.e., not stepping the voltage down as much), allowing more voltage to be delivered to the load, which represents an increase in power output over that produced by the Class A scenario.
To keep the thread on track then, a change in bias voltage that moves a design from Class A operation to Class AB operation, can in fact ultimately result in a significant increase in power output. But it is hardly created by the shift in bias voltage alone. As previously stated, the bias voltage that a given tube requires in a given application is merely a means to an end. It is no different in this case, either. The shift in bias voltage allows the use of greater B+ voltage and ultimately a lower load impedance OPT for the tubes to operate into, that together creates the increased power output developed.
Dave