Just looking at the specs, the KM comes in fewer sizes (making fit a little less precise) and weighs more. The LHT has more head tube to get the bars higher and lower BB. CC has shorter wheelbase which yields less stability. LHT has a more lax head tube angle. LHT has more water bottle mounts and dual rack/fender eyelets front and rear. LHT is built for 26" wheels in smaller sizes to avoid weird geometry.
Any of them will work on or off road, but the LHT is just better designed for more hours in the saddle.