In real life all it took was bullets to pierce the gas tank, controls, pilot armor, pilot, fuel lines, wing radiator lines, hydraulics, you name it.
In AH the round stops at the "skin" of the plane, and adds damage to it. Once damage passes the "critical point" (whatever HTC has that set to) the part pops off. There is internal damage but it's limited.
So the reason it's harder to shoot things down in AH is because it's greatly simplified what can be hit, and how many hits equal "the part falls off".