The PIC* in a helo sits on the right because helos are inherently unstable. While you can put some friction on the collective and let go, letting go of the cyclic is a bad idea. So if you sit on the right, you can use your left hand to tune radios and the like. Since the controls aren't mirrored, sitting on the left would mean you would have to "hand off" control of the cyclic to yourself everytime you wanted to twiddle a knob on the IP or overhead panel.
Tiltrotors use the same approach for the same reason. So the real question is why do fixed wing drivers sit on the left? My guess is that it's due to most fields using left-hand traffic, which I believe came from the horrid gyro-coupling exhibited by airplanes in the early rotary engine days.
*obviously, you can be PIC from either seat, but I'll just use that term to describe the customary usage.