It took a little time for me to tweak my Kemper rigs before using them in a live situation as well. I tweaked and listened to my amp rigs using studio monitors, studio headphones, custom ear molds, fx loop input on combo amp, powered Mackie p.a. speaker, and even rented a rehearsal room for 2 hours to listen through a p.a. Granted, this is probably more than most people have access to on a regular basis.
What I found was that the rigs always sounded slightly different and I wanted to tweak them accordingly. I decided to start eliminating some of the variables by using fewer amp rigs, limiting myself to about 10 that I liked the best. Then if the tones were similar, i.e. medium gain or high gain, I would find the cabinet profile I liked the best and the same cabinet profile for different rigs when I could. When the entire rig changes, sometimes there are eq curve differences and it takes about 15-20 seconds for your ears to adjust and in the meantime, it sounds "weird".
When I play live, we use in-ear monitors, so it's a pretty flat, even response except for the midrange bump in the resonant frequencies of the molds themselves. So between the ear monitor signal I get and tweaking to a powered p.a. speaker at home and limiting my work to as few amp rigs that I need to get by, I was able to get some great basic sounds. I eventually got an Atomic Reactor FRFR tube powered wedge and I've been using that to tweak sounds at home and for stage monitoring at smaller gigs where I don't have ear monitors. The problem with being dependent on floor wedges in most monitor systems is that the eq's are carved up heavily to keep vocal mics from feeding back, which murders from the Kemper.
If you can work diligently through the initial tweaking process and get a decent FRFR powered speaker, you can dial up some pretty amazing tones that are consistent from night to night and get even better as time goes by as you fine tune in the live environment.