The Klippel automated method and Spinorama charting tell you a LOT about the speaker but there are still differences that you can hear which must somehow be buried in the fine detail of these measurements. The measurements don't seem to properly weight all the features that a human listener seeks in the sound.
For example, take two Revel speaker models which look quite similar on the spinorama and listeners will be able to hear distinct differences. ( Revel uses spinorama to optimize their sound, which is why I picked them for the example - there are surely Revel models which look very similar on spinoramae )
Likely whatever the human listener is hearing CAN be measured - these factors are probably somewhere in the data - but bringing them out to view on a chart is so far an inexact science.
The spinorama coupled with the Klippel robot seems to be the best tool so far.... but it is based on steady state measurement, and it would be good to also know more about speaker behavior in the time domain; after all music has lots of short duration events in it and characterizing the speakers behavior in regard to these signals would likely add quite a bit to overall characterization of the speakers sound.
Waterfall plots kind of start down this road but present almost too much data, data for which we don't really have proper analysis methods. You can see resonances and gross stored-energy problems but I think there is a lot more we need to know about this facet of speaker behavior- how does it respond to short duration events at various frequencies and at various output levels. Some new methods are needed.