A very likely reason two amps can sound different, yet measure similarly on the test bench, is that the measurements typically taken are not done under the real load an amplifier will encounter with a dynamic waveform. Secondly, I'm not sure the typical bench measurements are measuring the right things regarding how an amplifier will sound. For a simple example, what if THD is basically the same, but the distribution of even and odd harmonic distortion is different among the various amps. Or what if various parameters, alone perhaps not significant, combine in ways that alter our brain's interpretation of the sound?
I think it's a not so simple a question you've asked. In my opinion, the best amplifier manufacturers have a basic measurement model they've developed/trust that allows them to accept or reject a given design before putting much additional time and effort in developing it. I would also guess that any manufacturer that claims to develop a design soley from ear, beginning to end, is probably not being truthful, spent a lifetime getting one design "right", or will not have much consistency in future designs. My point is that an audio system is a complex system, much like the weather. We can know quite a bit about the "averages", but it takes a very complex model, with alot of measured inputs, to have a reasonable chance of predicting the weather with any degree of accuracy.
I think it's a not so simple a question you've asked. In my opinion, the best amplifier manufacturers have a basic measurement model they've developed/trust that allows them to accept or reject a given design before putting much additional time and effort in developing it. I would also guess that any manufacturer that claims to develop a design soley from ear, beginning to end, is probably not being truthful, spent a lifetime getting one design "right", or will not have much consistency in future designs. My point is that an audio system is a complex system, much like the weather. We can know quite a bit about the "averages", but it takes a very complex model, with alot of measured inputs, to have a reasonable chance of predicting the weather with any degree of accuracy.