I don't think that you need the original Falcon for OpenFalcon or FreeFalcon. My friends managed to install them alone. But that's about one and a half years ago. Try it yourself if you have a fast connection.
FreeFalcon and OpenFalcon - multiple aircraft, multiple campaigns, updated graphics. Red Viper add-on has added some stuff like SAM operators firing without radar locks in formations when the visibility is good, and other new AI tricks.
Allied Force - more stabile, but costs money (should be cheap nowadays). No updates coming - I find this good, though you might disagree. The only thing I wish they would do would be update of the graphics (especially terrain) and multiprocessor support, but no such luck. But I think it is good enough already.
Of course in Falcon the aircraft trims itself and you don't have to worry.
Except when it gets damaged and the control surfaces get stuck. If you haven't flown 30 minute returning trip to home damaged and haven't applied full banking force with all the trim maximized, you are missing something. Especially when the flight control system changes the stick gains when landing gears are extended and locked (barrel roll at ground level anyone?). I missed the runway twice but just barely managed to land the aircraft at the third attempt (declared emergency, of course).
I have also played Freespace 2 with keyboard only. Despite of that, I cannot even think of flying Allied Force without joystick. My understanding is that pilots are discouraged from applying rudder control when flying a real F-16 (exception of landing) - above 400 kts (something) rudder doesn't even move due to FLCS intervening! That might explain your differences.
Did I miss something? Anyways, if you took Allied Force, you could fly occasionally with us. PM me about this (I live in Finland so time zones...)
Falcon 4 and derivatives really require a lot of effort in learning the simulation (this is not really a game any more), but rewards the enthusiast by never repeating itself. And that massive air war thing going on around you is something you don't find anywhere else, short of being a real pilot yourself. I'll be replying if you have some questions and/or I find out that I indeed missed something.