We should drop "gyroscope", as it too vividly conjures pictures of a spinning top toy, but I claim that the angular momentum of the rotor remains an important, defining property. If it wasn't, then you could roll or pitch the machine as fast in rpm as you can yaw it, and I don't believe that's nearly the case.
The pitch and roll rates achievable in modern, semi-rigid rotor systems are much higher than those for teetering or fully articulated rotors. This is all to do with the rotor head design and little to do with precession or angular momentum theory.
The distance between the flapping hinge and the rotor hub dictates the control power (which can be loosely defined as how much you have to move the cyclic to achieve a specified change in attitude of the fuselage). Where there is no mechanical hinge (Lynx for example which uses the flexing of the titanium rotor head) an 'effective hinge offset' is given as a percentage of the distance between hub and blade tip and represents where a mechanical hinge would have to be to achieve the same control power.
So the pitch and roll rate of a helicopter is not limited by precession, it is limited by its rotor hub design and its control power.
On a teetering head the fuselage follows the rotors under the influence of gravity (hence why low G is so dangerous as you have little control over the fuselage position), with mechanical or composite hinges you create a lever whereby moving the blades provides an equal and opposite reaction on the fuselage.
Awblain, perhaps you should look at how the pitch change mechanism works - a pitch change rod following a swash plate produces a sinusoidal vertical movement akin to a piston in a cylinder in a car engine. The movement of the pitch change rod is not constant, it has two stationary points (like top dead centre and bottom dead centre) and accelerates and decelerates between the two. Hence the rate of pitch change (and therefore its resulting aerodynamic effects) are at maximums 90 degrees from the point where the initial change is made (ie from the TDC or BDC).