Again from the pilot's viewpoint, "stability" and "agility" are often perceived as opposites (though from the engineering viewpoint they are not, exactly).
For example, the stock Bensen/Brock gyro was beloved by many hot-doggers for its quick control response and light stick pressures. These qualities stemmed, I think, from the lightweight, high RRPM rotors that Bensen used (RRPM > 400 at 1G). Such a rotor has low rotor damping and indeed the rotor follows control inputs quickly.
It also, on the downside, does not resist PIO and PPO as well as a gyro with a slower, heavier rotor. say , for example, that an unintended nose-down rotation starts (whether in PIO or PPO). If the pilot holds the stick still, the light, fast rotor just follows right along instead of resisting a bit.
In contrast, a rotor such as a McCutchen, with more diameter, lower RRPM and more mass, has more rotor damping (lag) than a Bensen. It's not unusual for a McC. rotor to lag enough that the pilot gets 2/rev slap-back in the stick when he/she makes rapid, reversing lateral inputs. The rotor can't get out of the way of the moving rotor spindle and so hits the teeter stops (the teeter stops travel with the spindle).
DON'T make rapid, reversing fore-aft inputs, please! And keep in mind that rotor damping is proportional to rotor thrust. No thrust, no damping, no matter how fast the rotor aligns itself with the spindle. That's one reason that rotor damping alone is not a foolproof PPO-preventer.