This is the simplest and quickest way for me:
First connect the SPDIF output of your KPA to the Akai DPS-24 SPDIF input or use any other audio device you have available for recording. Setup everything to profile one amp where you noticed the issue you are talking about. Take a profile and refine it, but don't save it. Once you are happy with the results and before you save it, hit record on your DAW or audio recording device and play with your guitar the same thing, switching between the profile and the reference amp using the buttons the KPA offers for that purpose while profiling. Play switching back and forward from the reference amp to the profile until you think you have captured what you want to demonstrate. You can then edit your track to only contain those parts that show that clearly and you are done.
That is what I do to compare when I take my profiles. What Audioholic suggested would be more accurate but probably not so straight forward.
This is also what i would suggest if you are not that much into recording. At least you have an identical recording chain out of the KPA this way.
To make a real fair comparison you would have to reamp the same DI input file into both setups. This can be little tricky though.