For the MI-8, switching the tail rotor from the right side to the left side increased its efficiency. It's all the exact same parts, they just flipped the gearbox around 180 degrees starting with the Mi-8MT, the same version that also got the TV3-117 engines instead of the older TV2-117 engines. Previously, the tail rotor rotated "with" the airflow from the main rotor, and when flipped, it rotates "against" the airflow from the main rotor, which increased its efficiency.
Basically the same thing happened with the Huey.
EDIT: Should have said effectiveness instead of efficiency, but probably both reasons really.