From a rubber viewpoint, I would think that puncture resistance is diametrically opposed to traction. A soft, flexible rubber works better for traction, as it deforms to the road surface (bulges into small depressions, and the opposite over small bumps.) It 'grips' the road surface. A hard rubber would not do this as well.
However, a hard rubber would tend to deflect thorns and road debris better than a soft rubber - to better keep them from penetrating through into/through the tube.
I would think that all else being equal, a hard rubber would have lower rolling resistance than a soft rubber. (not deforming as much would mean less internal friction.) However, this also means that it would have a somewhat harsher ride.
The Town & Country would definitely have less high-speed cornering traction than the slick Kojak though. You have no tread over substantial portions of the outer portions of the T&C.
Also, if using a friction drive, the T&C has slightly more vibration than a slick tire. I had an Inova Swiftor on the rear of my Staton friction drive, and it had great traction, (including cornering,) NO vibration, and increased the top end by a couple of miles per hour. But, I locked up the rear wheel in an emergency stop from 25 mph one day (my old bike had coaster brakes on the rear,) and the road
ate the soft rubber, right down to the fabric in the plys!