In my opinion, this is one area where the KPA has an advantage. With profiles, you know exactly what type of tone that the mic'd cab was designed for specifically because a profile is a snapshot of the entire rig, not just a single component of it(a la IR's).
Unfortunately, when it comes to IR's, I often feel like I'm groping in the dark
I agree that it can be an advantage in this particular sense described.
That said, for me there's other challenges that come along with kemper. Some have no issue finding many profiles they like and hence use. For me (and plenty I know), profiling rigs is the way to go.. almost entirely, with relatively few profiles as exceptions. That can be quite time consuming.
With axe fx I have much more possibility to get what I want without that much "real world" work. Before, it was more possible for me to put in that "analog work" to get the profiles I need for a given purpose, using particular pickups, tuning, right level of gain and all, as I was in an environment that could accommodate this.
But the less that has been the case.. the more I've liked using axe fx, I would say.. ease of use, convenience has become a big thing for me, for my needs and what I want to achieve. At that point, I have quite particular IRs in mind too, so the issue described is not so much a problem for me. Even with kemper, from some point on, I've most often used IRs, I would say, and direct profiles.
On Axe Fx, part of the challenge has been firmware updates changing some tones too much... But I tend to create a lot of tones over and over, so that's no a deal-breaker I would say; and libraries of profiles have been less convenient for me overall. Of course, I still like kemper quite a bit for what it does too, for sure, and see myself using it more when closer to amps again, especially for keeping certain tones intact.