I had a Kemper for 2 years. Axe III is better in EVERY CONCEIVABLE WAY. Seriously, profiling is NOT better technology. In fact, there are too many disadvantages of profiling to list, such as having to wade through hundreds, if not thousands of profiles just to find a few you like. And, you have to find a profile you like at each gain level you would use, for each amp you use.
I don't own a Kemper, but when I imagine the prospect of finding an amp tone the same way I currently have to find an IR I like... yikes. No thanks.
While I generally love dialing in amp models and effects, IR browsing is easily the least-fun part of the entire process of building a virtual rig. You just blindly click one IR after the next and hope it sounds good, on and on forever. Sure there's names and descriptors and whatever but they are of limited help.
Anybody who finds a way to allow users to dial in an IR with speaker parameters, number of speakers per cab, cab size, etc. the same way they dial in amps and other effects is going to make some serious money. I have no idea how you'd even start that process but hopefully somebody figures it out. Imagine being able to start with a generic 4-speaker guitar cab and being able to "dial in" a Vintage 30 loaded Mesa oversize or a Greenback loaded Friedman using parameters for magnet size, cap size, cone material, cab volume, whatever.