When two amp sounds sound the same, than it is impossible that one sound will drown in the mix, while the other doesn‘t. If these sounds behave differently, than they simply do not sound the same, no matter what a pro says.
And yes, this might be about high frequencies and transients, as some users state in this thread.
If there were esotheric parts in the sound, that would make a difference in a busy mix, then those parts would easily be identified, when listening solo, especially for a pro.
I would suggest that the profiling process will capture the dynamic response as well. The ability to translate the transient to the speakers would likely be more a property of the amp and speaker being used. I believe that the actual signal contains the accurate transient response in most cases.