It would take several hours to properly discuss the topic of yaw stability in aircraft. Frankly, I have neither the time nor the desire. However, here are some basics that can explain how two very different aircraft under very different conditions might have a different outcome from a similar failure.

First, the basics of natural stability in the yaw axis of an airplane are similar to that of a model rocket. You can go to that site to read a good explaination of stability in layman's terms.

There are three different conditions for yaw stability. They are positive stablity where a displacement is countered by the plane's stability and it tends to return to straight flight, neutral stability where a displacement remains unchanged, and negative stability where a displacement tends to get worse.

Normal planes are designed to be positively stable in all three axis. Some competition aerobatic aircraft are designed for slightly positive or even neutral stability to make them more maneuverable, though this is at the expense of being more difficult to fly. Some aircraft like modern fighters are actually designed to be naturally unstable in order to increase performance and maneuverability. These aircraft depend on fly-by-wire systems. Without these systems, the planes are completely unflyable.

The stability in the yaw axis depends on the relationship between the center of gravity (CG) and the center of pressure (CP). Positive stability requires that the CG be ahead of the CP. If the CG and the CP are colocated, then the plane will have neutral stability. If the CP is ahead of the CG, then the plane will have negative stability.

The CG is the point of rotation for the aircraft. The CP is best explained here. In simple terms, you calculate the profile area of components and their distances from a reference line then run some math to determine the CP. In a nutshell, profile area ahead of the CP, such as the foreward fuselage, tend to move the CP forward and are thus be destabilizing. Profile area behind the CP, such as the rear fuselage and the tail surfaces, tend to move the CP rearward, increasing stability.

Other objects on the plane can be stabilizing or destabiling depending on their position related to the CG. If the engines are mounted on pylons that project in front of the CG, then they're destabilizing. If they're mounted more to the rear, then they may be slightly destabilizing or even slightly stablilizing depending on the geometry. One thing is certain - if you lose your vertical stabilizer and rudder, then the CP is going to move forward in a hurry. The final stability will still depend on the relationship between the new CP and the CG. In most planes, the CP will be ahead of the CG rendering the plane unflyable.

Now, lets look at the two aircraft involved in the incidents. The JAL plane was a Boeing 747-SR46 as shown below. This was a version designed for short range missions with a lot of passengers.

I don't know exactly where the CG is on the 747SP, but a guess would be roughly near the emergency exit over the wing in the photo (outlined in white). Looking at that photo, it appears that the profile area of the rear fuselage is much greater than that of the foreward fuselage, even accounting for the famous 747 hump. The inboard engines and pylons are ahead of the CG, so they'd be destabilizing. The outboard engines and pylons are behind the CG, so it appears they'd actually increase stability slightly. Next, there's the question of how much of the vertical stabilizer and rudder came off in the JAL crash. If it lost all of the vertical stabilizer and rudder like the Airbus crash, then the CP would move foreward. I don't know the final position of the CP, but I suspect the plane had at best neutral stability (making it a real handful to fly) or perhaps slightly negative stability.

Now, let's look at an Airbus A300-600 like the one that crashed in New York.

The ratio of fuselage area ahead and behind the wings appears to be about the same as the 747SR. There are only two engines that are mounted well ahead of the CG, so that would be destabilizing. Beyond that, there isn't much that would help the stability when the complete vertical stabilizer and rudder came off like it did in the crash. At best, the plane would have neutral stability. More likely, the plane would be completely unstable and impossible to fly.

There are so many other differences between the two crashes that it makes little sense to compare them. The JAL flight was at cruise altitude and airspeed when disaster struck. The AA plane was only about a minute after takeoff, so it was flying much slower and probably with the flaps extended about 10 degrees. The low airspeed decreased the effectiveness of the remaining control surfaces and they had no altitude to attempt recovery. The JAL crew had perhaps a slightly more stable plane, more effective controls due to the higher airspeed, better ability to try thrust vectoring, and much more altitude to work with. Even then, they still couldn't fly the plane.

One thing that puzzles me is why you seem to latch on to every conspiracy theory out there, especially when it comes to aircraft accidents.