The engineering term is "slew rate" measured in volts/microsecond. It answers this question: how fast can the output stage move?
The "pro" argument -- and it is a valid one -- is that if an amplifier has a fast slew rate, it will have a wide bandwidth, and therefore the phase shift at all audio frequencies will be negligible.
The "con" argument is that wide-bandwidth amplifiers, such as the Kenwood Super Eleven, are always attempting to turn into oscillators at frequencies like 500kHz. Sadly, as amplifiers age, component tolerances drift, and the circuit board itself may acquire a lumped reactance. A great many machines are no longer unconditionally stable. They may "blow up" during power up, or when hooked into a load with a "difficult" reactance, such as electrostatic speakers.
This problem is exacerbated by the unavailability of many original parts, and the necessity that substitute parts be used for power amp repairs, thus making the amplifier even more susceptible to instability.
Fred