For anyone unfamiliar with basic suspension setup, the following rambling might help you to get acquainted and understand my comparison of PSS10 vs. stock PASM later. Keep in mind my day job has nothing to do with auto mechanics and therefore please take this discussion with an extra large size grain of salt. Expert opinions and corrections welcome as always.

It's probably easier to understand suspension setup if you categorize it to 2 primary parameters:
1. Pitch and roll control. Pitch is front to back vertical motion; roll is side to side. More stiffness means less pitch/roll.
2. Bump management. How the car absorbs bumps on street.
If you think about it, 1 and 2 actually represent handling and ride respectively. Increasing 1 affects 2 adversely.

The coilover has 2 main components, a spring and a damper. The spring is the prime determinant of how stiff you want your car to be. While the damper is there primarily to dampen the spring's motion, it *also* affects stiffness. There are then 2 ways that the coilover's overall stiffness could be affected:
A. By changing spring rate.
B. By changing the dampening rate.

Bilstein increases stiffness the old fashioned way: by using a stiffer spring. That is, A above.

PASM increases suspension stiffness by increasing the dampening rate, B above. From my questioning of people who set up suspension for a living, this is not necessarily the best way.
In addition, in standard practice the dampening rate is usually set to *match* a particular spring: That is, there is one "correct" dampening rate for a particular spring in a particular car. In PASM, you are basically using 2 different dampening rates, vastly different as a matter of fact, for a single spring. This implies one of the 2 settings involves a compromise; in the Turbo I think this is the FIRM setting.
Lastly, I think that to affect large change in suspension stiffness, the dampening rate of the FIRM setting has to be increased so much that it overwhelms and makes the car behaves as if there is almost no suspension flexibility left. When the car hits a bump at high speed, the tire tends to lose contact (airborne) easily. In a mid corner bump, this would make the rear end "walk" laterally.

The point is this: I hope now you could see that even though Bilstein PSS10 and PASM- FIRM both increase stiffness; the methods they use are dissimilar (spring increase versus damper increase) and therefore their "character" when it comes to bump absorption and pitch/roll control are completely different from one another.