It's NOT that you simply select your favorite AxeFx patch connect the KPA and profile the whole thing.
The profiling captures the amp/eq/cab/mic stuff only - not any of the effects!
There are some more steps involved for example:
-switch off all effects (beside EQ's, amp, cab)
-switch the AxeFx to mono (the KPA can profile in mono only - no way to profile huge stereo double amp AxeFx settings)
-switch of noise gate
-Avoid more than one 'distortion part' (switch off drive blocks, speaker drive, if the preamp is overdriven avoid that the power amp is overdriven as well)
-Switch off room level in the cab block
...
Note: all these steps may have a huge impact on the AxeFx sound anyway - but the result you get NOW from your AxeFx can be profiled.
Then carefully setup all levels so that both the AxeFx and the KPA do not clip. (the KPA shows a warning in case this happens).
--profiling--
After this can the results be compared - in most cases you still hear a difference.
Here we come to 'refining'.
We can play some cords on the guitar and the KPA adjusts something (whatever) to match the sounds closer.
In addition are there some amp parameters to play with to match them closer 'by ear'.
After all this we have our new KPA profile from a part of an AxeFx preset.
The next step would be to try to recreate the other parts of the AxeFx.
In case the KPA has similar effects (drive, chorus, delay, reverb) then we get good results.
But note: The AxeFx has WAY more effects, effect types and parameters - so in case you need A LOT of effects in your patches - and/or have them NOT all in one simple row - you WILL NOT be able to recreate your AxeFx sound with the KPA.
The same is true (as mentioned above) for true stereo or two amp setups.
If all you want is a simple setup like wah-drive-amp/cab-chorus-delay-reverb - then you may come very close to your sound.
Update:
Done - all my AxeFx presets are profiled