I find that having HPF/LPF set correctly makes a big difference in consistency. When just playing a live cab, it doesn't make as much difference as when I am using studio monitors or through a big P.A. I have different outputs adjusted for "Live" and "studio".
The way I set the LPF that helps it to sound like an "amp in the room" recording/studio monitors is I listen to my cabinet as I turn down the LPF. As soon as I hear it affecting the high end, I stop there and go up a little higher. (usually around 8K) That keeps frequencies that would normally not be heard with a "real" cab out of the recording/studio monitors for a more "natural" sound. Every speaker setup has a different crossover, EQ etc.
I imagine if you set up your Kemper with a perfectly flat set of monitors then played it through a perfectly flat P.A it would be the same, but most P.A. systems are not flat by any means.
If things sound different between setups, like it has been mentioned, it's not the Kemper's fault, it's the differences in what it's going into.