Well, I am a newbie here as far as scale helicopters, but I have thousands of hours piloting and giving instruction in full size helis, and both scale and full size have the same aerodynamic principles.
With a rigid system you basically have a fixed unit between the rotor head and rotor shaft (mast). The blades have some give (flex) but when the head moves, the mast does too, which in turn moves the fuselage, all as a single unit. With flapping blades in a multi-blade system each blade floats independantly of the others. This is usually called a fully articulated system. A flapping two-blade system is usually called a teetering or semi-articulated system, like a see-saw. When one blade goes up the other one goes down. These floating systems allow the mast to hang below the rotor head without forcing the mast (and fuselage) to tilt with the plane of the rotor.
With rigid rotor systems the mast/fuselage combination tilts in the direction the rotor head tilts. With flapping or articulated systems the mast tends to remain perpendicular to the earth and the tilting of the fuselage is caused by acceleration and deceleration (fore and aft) and by centrifugal force in turns (left and right banking).
If you bring a helicopter with a rigid rotor to a hover and then move the cyclic stick slowly to the left or right the rotor will tilt in the same direction but the fuselage will also tilt that way. If you make the same maneuver with a teetering or articulated head the plane of the rotor will tilt the same direction as the stick and the helicopter will begin to move in that direction but the fuselage will tend to remain perpendicular to the earth. It will only tilt from acceleration.
The biggie here is that the rigid rotor system limits the travel of the blades up and down (particularly down). This is essential in aerobatic maneuvers such as as inverted flight 3-D, etc. If you tried to fly inverted with a floating system the rotor blades most likely would cut off the tail boom. Almost all civilian helicopters use variations of articulated, semi-articulated and teetering rotors. In scale helis it should produce more realistic flight.
I am under the impression that most flybarless gyro systems work by sensing the tilt of the helicopter. Since a helicopter with a flapping blade rotor head tends to have much less fuselage tilt I am not sure how effective FBL gyros work with them. Maybe someone with experience using flybarless gyros with a flapping blade system can enlighten us.
I am probably making this post tedious to read, but there is another important consideration, that of Center of Gravity (CG). In most helicopters, the helicopter should balance perfectly level if you suspend it with a string from the center of the rotorhead. Lets say you have a helicopter with a rearward (aft) CG. If you come to a hover with a helicopter with flapping blades the helicopter will hover with the tail low and the center of lift will be in the center of the rotorhead. If you bring the same helicopter to a hover with a rigid rotor, the helicopter will tend to be more level since the rotorhead/mast combo is forcing the fuselage to follow it, but the center of lift will move rearward to some point along the trailing blade as it crosses the tail boom. This causes the rotor system to have an asymetrical lift pattern which can be very noticable in the controls. The helicopter is usually overly sensitive in certain areas.
I tried to keep it fairly simple and left out some other factors such as gyroscopic precession, etc.
Hope this wasn't too boring!
Retired Commander - Georgia State Patrol Aviation Division (UH-1H, Bell 407, Bell 206BIII, OH-58A)
Scale VH-60N/Trex 600ESP, HH-60J/Trex 600EFL, Hughes 500D/Trex 700E, Century Bell 47G/Trex 550E
Trex 550E, Trex 450E