The premium version also differs from all other versions in that it has the KDSS suspension which controls the sway bars.
KDSS is available on both the TRD OFF ROAD and the TRD OFF ROAD Premium. (LC as well)
I don't know what tires come on the other trims, but the all-terrains that came on my off-road premium have handled surprisingly well.
The TRD OFF ROAD Premium comes with "Mud and Snow" tires. Only the TRD PRO comes with All-Terrains.