I can't comment on comparing the KP to the FX as I've not tried the later.
I'm just here to say that was quite surprised to hear someone say that they thought these were used "exclusively in a live setting". It had always that of this as mostly a studio tool.
I know guitarists in working bands that have both, but leave them in the studio for recording and still bring their traditional rig for live gigs.
However, when I researched the KP deeper for my recent purchase of one, I was exposed to lots of testimonials of people using them (amp version or not) in live settings and thought "huh, why not".
But exclusively for live? As in not using it in the studio? I don't get that.