Then you should check your methodology for creating profiles. If you hear a unique signature of tone on the KPA in your profiles it must be due to something you are not doing right. Maybe you signal chain when doing profiles is introducing that signature tone you are referring to. If you are sure it is not that you may share a few clips where you demonstrate this comparing the profiles with the real amps.
I have owned the Axe FX II for a year as well and the KPA since January. I did not compare them with each other often but instead with the real amps profiled/modeled because that's what it matters.
MadH,
I have no quarrels with you or anyone else here. In my own personal profiling (which I have done over 150 times at this point), I have noticed that the KPA usually imparts a bit of it's own DNA when I compare the final results - this is not a problem for me because I almost always like the final result once I've tweaked it to my personal preferences. (I am referring to the basic nature of the distortion, as opposed to EQ or Cab matching issues). But I would disagree with anyone who says that the KPA is a totally transparent, tonally neutral sound generation device - and WHO CARES, as long as the tones are usable and pleasant to the ear - I was just making what I felt was an obvious comment about the current state of all the modelers I have tried to date...