I know the question wasn't targeted at me but I can explain my method of comparison as it might be useful information.
I wanted a fair fight so I put the JP2C through a Suhr RL into the Mikko 2 cab sim plugin while putting the Axe model through the same cab sim. I took care to be really precise with all the amp settings which I took from a JP video. With the same settings plugged in the difference to my ears was a few percent at most and we're talking isolated here, not in a full song context. The thing that really sold me on the quality and precision of the model was the distortion texture which was 100% spot on. The slight differences in tone (BMT) could also be chalked up to the fact that even between the same physical amps there is a part tolerance for pots and other components which can contribute much more. But, comparing my own JP2C to JP's own JP2C (which the Axe model is based on) it was literally splitting hairs.
To get to the point, since in this comparison both the physical and modeled amp's power amp section is utilized I highly doubt that comparing through an SS PA would yield any difference. I didn't have the chance to compare other amps to their modeled counterparts but the JP2C model is certainly as close as it gets and if the same is true for other models then the Axe III is simply the first modeler to achieve singularity