I've been curious as well as I've been trying to decide between buying a Luke III (or Luke II with EMGs) or Axis.
From what I read, the bridge pickup of the Luke III is a custom-made Dimarzio pickup, and sounds close to the Dimarzio Norton. The neck (and middle pickup if HSS model) sounds like Dimarzio's Injector pickups (Paul Gilbert's signature pickups).
The luke3 has dimarzio transition pickups. I've recently traded my axis super sport for a luke3 and while the axis was great, I think the luke3 is better. The range of tones is immense, had lots of compliments on my sound since changing. Sorry I can't a/b the pickups as the construction of the guitars is so different, but both are great guitars.
Check this out on the Dimarzio website. Allegedly, the Axis pup is most similar to the Tone Zone. That being said, one could compare the output levels of the two in order to discern their capabilities.