As BBB said, the trials tires are nice, but not for spinning.
I have (2) KDXs, one with a plate for the few times when OHVs are not allowed on roads between trails.
Both KDXs run Dunlop 803 trials tires, which have the softest knobs, but I run at higher pressures (10-12psi).
Love the tire off-road, but they develop cracks at the base of the center knob, supposedly due to running at higher speeds. I would not put one on my KX500.
That being said, I had to ride the KDX back to the truck on a section of Bouquet Canyon Road which is a nice, curvey section of pavement populated by racers and sportbikes. I surprised the heck out of a bunch of canyon racers by staying right with their pack in full off-road gear. The 803 stuck like glue and I got rid of all the chicken strips on that run.
My KX500 runs a Maxxis IT for off-road and it's been great on the occasional street. It's not rough at all but I had to really convince the guy at Cycle Gear to balance it. For any riding, the key is balancing the wheel/tire - either lots of weights or a second bead lock.
I have a second set of wheels for the street for the 500 (plated), with an 18" rear. Bought the cheapest DOT dual sport tires (DURO) and have only put them on twice. Let's just say I have more confidence running the Maxxiss ITs on the pavement.
Bottom line, decide what kind of riding you want to do and pick the tire for that. The best is to have 2 sets of wheels with the best choice on each. Try talking to guys that ride DRZ400 or XR650s and such. Maybe advrider.com
Dunlop 803s on the KDX with DURO D/S tires for the 500 in the background...