I haven't owned both, but I did drive the heck out of 3 KJ's before I got the KK. Went to CarMax looking for a wrangler, but none that I liked were there. So, went trying KJ's. Found one limited, and two sports. (No Rennys

). I kinda liked the small feeling of the KJ, as it reminded me of a Suzuki Samurai. Yes I know they are tiny, but that's just what I was thinking of at the time. Honestly, the one good one (of course it had to be black) was pretty nice. Boring interior, but the engine sounded great. I agree it had much better throttle response. I liked that for the on-road, but don't know how much I would like that for mud/snow.
The insides of the KJ felt tiny compared to the KK. Especially after I've gotten used to the KK. The only thing I reeeeeally like better about the KJ, (of course having all those aftermarket parts available is nice) is the weight. At least it weighs less than the KK. This would be fine, if the power were up a good 30hp.
Final Thoughts: KK is a wonderful mid-size SUV. Jeep, actually. It's just underpowered for it's weight. And the suspension is TOO soft.