Most engineering designs are trade-offs, and designing for quick transient response is no exception. Light weight means, generally, a small engine. Low PMI means, generally, placing the engine as close as possible to the centre of mass (CM) as possible. So, many quick response cars are mid-engined, further constraining engine size. With engine size, we get into another trade-off area: cost versus power. Smaller engines are, generally, less powerful. The cheapest way to get engine power is with size. A big, sloppy, over-the-counter American V8 can cheaply give you 300-400 ft-lb of torque. Getting the same torque from a 1.6 litre four-banger can be very expensive and will put you firmly in the Prepared or Modified ranks. But, a bigger engine is a heavier engine, and that means a beefier (heavier) frame and suspension to support it. Therefore, the cheap way to high torque requires sacrificing some transient response for power. This design approach is typified by Corvettes and Camaros. The general rule is that these kinds of cars get you out of a corner more quickly because of engine torque.
So, we can divide the sports car universe into the lightweight, quick-response-style camp and the ground-thumping, stump-pulling-style camp. Some cars straddle the boundary and try to be lightweight, with low PMI, and powerful. These cars are usually very expensive because the fundamental design compromises are pushed with exotic materials and great amounts of engineer time. Ordinary cars are usually mostly one or the other. No one can say which style is "better." Both kinds of car are great fun to drive. There are some courses on which quick-response type cars will have top times and others on which the V8's will be unbeatable. Fortunately, these two styles of cars are usually in different classes.
Let's back up that discussion with some physics. What is transient response and how does it relate to polar moment of inertia?
Any object resists a change in its state of motion. If it is not moving, it resists moving. If it is moving, it resists stopping or changing direction. The resistance is generally called inertia. With straight line motion, inertia has only one aspect: mass. Handling is mostly about cornering, however, not about straight-line motion.