My feel is that it depends on the profile. Generally speaking, the KPA can make a "bad" guitar sound appropiate. Do you share this impression?
Short answer: It depends on the profile.
Better answer: It depends on the amp and its settings that were profiled.
I mean, some real amps at extreme settings will make alot of guitars sounds similar.... and if thats the amp sound/behaviour you want to capture, the KPA will do it. If its not, get a good profile of a more honest amp and setting, and changing guitars will have the expected result of better showing the instrument differences.
The good amp profiles act just like their captured hosts. If well captured, the profile keeps the honest quirks/personality (both good and bad) of the original amp at that setting.
IMO this is the single biggest reason the KPA see's so much pro use in both studios and on stage. It's honest to what was going on during amp profiling.
A super sensitive amp that typically highlights individual guitar differences will do just that when well profiled. An amp/gain setting thats setup to sound similar no matter whats stuffed into the input jack will profile and duplicate that behavior.