On a chopper, even when the pilot sits on the LH seat the collective is on the left and cyclic on the right. One of the reasons the pilot generally seats on the right is at the beginning, the choppers didn't have any SAS or AP, hence the cyclic must be held permanently, whereas the collective can be locked in one position, making the left hand available for other tasks like radio, carb heat, mixture and so on.
There is no general rule, it all depens on the type.
Cheers
ATN