[Driven97]

What's missing from Bill V's graphs is what the axes are.

The y-axis is shock force. On top is compression (bump), on the bottom is extension (rebound.)
The x-axis is shaft velocity.

The left side of the charts is low shaft velocity. This means transitional stuff. Getting on the gas, getting on the brakes, turning the wheel. Weight shifting in the car. Dive, squat, and roll. Note shocks don't control the total amount of these things, they only control the rate at which these occur.

The middle of the chart is small or "soft" bumps - pavement cracks, expansion joints, or maybe track curbing.

At the right, high shaft speeds, is larger or "sharp" bumps. Poor pavement, large cracks, frost heaves, potholes, etc.

Digressive valved shocks build a lot of force in the low shaft speeds. Since they're "firm" in these conditions, acting as if the car had bigger springs. As stated above, this gives better body control in maneuvers. They then have valves that "blow open" at higher shaft speeds, which lowers the slope of the line / decreases the gain. This can let the shock be actually softer in large bumps than a linear shock, controlling the spring but without overdamping like an aggressive linear shock curve. Best of both worlds.

The big caveat is best of both worlds if they're done right. Getting valving close on a linear shock is pretty much by the book. If you know a spring rate & corner weight, you can pick 60% of critical damping piston out of a chart, and end up with a pretty good driving and handling car. Setting up a digressive shock is more of a black art. Picking the right shim stack that gets the right initial forces, puts the "knee" in the right place, even setting up the digressive valve shims can greatly affect the performance of the shock, the performance of the car, and the ride.

tl;dr a linear shock is fine for most people and driving conditions. A high quality and well tuned digressive shock will be superior in both control and comfort - but the hard part is getting there.