Axiom's DSP circuitry is programmed with the specific characteristics of the driver, so the amp is able to precisely control the driver without distortion.
I do not think that is correct. As you boost the signal using dsp/eq you also increase distortion. The big advantagesof dsp/eq is that you can extend the bottom end on the sub and control over-excursion.
As to whether or not you can hear the added distortion is not entirely clear. Certainly the EP600 compared to the SVS pb13 there is a lot more measured distortion as you get to the bottom end of the range, yet the sonic differences described in direct comparisons are subtle, at least for music.