In addition to the decrease in skidding with the dropped center, the reasoning behind this can also be explained with vectors. With only the center wheels and one pair of the side wheels touching in the dropped center design, the robot is turning about the center of those four wheels rather than the center of the robot. This means that if the force of the wheels are broken up into vectors, the rotational component of the turning wheels (portion of the vector perpendicular to the imaginary segment connecting the center of rotation and the wheel) is much larger in the dropped center than it is in the non-dropped center six wheel base. The other component of the force from the wheel is wasted because it is canceled out by a force from the opposite wheel on the bot.
Diagram:
In this diagram, the red arrows are the rotational component of the force provided by the wheels and X marks the center of rotation. In this particular moment, the top 4 wheels on the dropped center bot are contacting the floor and the bottom two are not. Note that the rotational vectors on the dropped center diagram are significantly larger than those on the non-dropped center bot, especially at the corners.