My qualifications are meager (a private pilot who hasn’t flown in years and whose helicopeter lessons were one hilarious and embarrassing story after another; a lifetime electronics and gadget hacker, who used to teach “practical electronics design”) However, I think that I can put some of the key problems into layman’s terms that might help.
Crudely: instability increases responsiveness and flexibility. It also increases, well, instability, which can be a deadly problem if your don’t have the power (or can’t rapidly and precisely increase the power) and rate of change (via control surfaces) that you need to get out of trouble.
An airplane has four primary degrees of freedom: three axes of orientation (aka “atttitude”: pitch, roll and yaw) and one of thrust. However, especially in the early days, when engines were less powerful and control surfaces were less capable, the three secondary axes (“slip” – moving one direction while pointed in another) were more important in critical maneuvers. The air craft were limited in their ability to "do as they were told, because of the limited strength of the available structural materials, available engines, and the need to devote [relatively] more of the available power to generating sufficient lift. Even today, a simple maneuver like maintaining a heading despite a crosswind, or climbing while level, requires use of “slip” relative to orientation, and it’s a basic pilot skill.
Airplanes were also designed for stability - the ability to self-correct to stable straight and level flight, predictably maintain a specific heading and orientation, etc. Now of course, in a dogfight, the ability to change orientation (heading) rapidly and unpredictably (unpredictable to your opponent anyway) can be very valuable. Also, let’s not forget the role of a jet’s high momentum in defining allowable maneuvers – it has a signifcant mass and high forward speed, but only air to “grab” to change its motion.
Today, after a century of experimentation and refinement of tactics, our best fighters are inherently unstable – that extra edge is now necessary, and we’ve developed fly-by-wire computers that turn the pilots control commands into predictable responses by implementing often counterintuitive actions of the control surfaces (like ailerons, tail flaps, extension flaps, elevons, etc.) A pilot couldn’t make all the necessary calculations, and certainly couldn’t make the necessary fine corrections many times a second. Such planes can’t be flown at all without the computer – they’d fall out of the air in seconds or minutes. (Though there has been discussion of making the control surfaces default to a relatively unresponsive and stable configuration in the event of emergency computer failure, I don’t know if that has ever been implemented, since computer damage would likely result from combat damage – a bad time to become a predictable brick)
Helicopters, however, rely strongly on SEVEN degrees of freedom for their design functions. The four primary degrees of freedom are obviously as important in directed flight or combat as they are for a fixed wing craft, but the three additional degrees of slip (motion independent of orientation) are also crucial. Helicopter take-off, for example, is pure slip – movement “up” while pointed “forward”, and key combat tactics include the need to hover behind a building or hill and “pop up” or “pop out” to deploy weapons (and then hide again). The ability to station-keep at a key location in a combat zone while changing orientation to track an object moving on he ground or in the air is also quite useful.
While I’ve simplified the helicopter’s controls to seven primary degrees of freedom (almost twice the simplified degrees of freedom of an airplane) the control surfacesand control [parameters of a helicopter are far more interelated. The speed and pitch of the rotors affects the counter-rotation torque (as the helo spins the rotors, the rotors try to spin the helo in the other direction: there’s nothing to “hold on to” in midair). The effects of adding power are more complex. The leading rotor (the one moving in the direction of the craft’s motion at a giving instant) is moving much faster than the craft itself, while the trailing rotor is moving much slower – each rotor is a separate wing flying in very different (and constantly changing) conditions, and they switch roles hundreds of times a second. This has required a much more sophisticated mechanical system to control all the factors in a predictable way. In a sense, a helicopter is already made manageable by a mechanical analog computer – and that very same mechanical “computer” that makes it flyable also limits its abilities
Crudely, you can consider each degree of freedom to add a “power” of complexity. if the problem iof maneuvering an airplane is X[sup]4[/sup], the problem of maneuvering a helo is X[sup]7[/sup] or X[sup]8[/sup] – probably more, because the mission of a combat helo routine demands it to change its motion (flight regime) rapidly (e.g. from hover to slip), within the limitations of the helo’s hardware abilities (e.g. rotor tips that can’t exceed Mach 1, engines that can’t instantly double their power with afterburners, turbines whose exhaust velocity adds signficant forward thrust when called upon to generate more lift power. etc)
I absolutely expect that helicopters will incorporate more fly-by-wire in coming decades, but I hope this grotesque simplification helps explain why it is a much more complex problem than the “sexier” (in the eyes of many) jet fighter.