On the LEFT, the RLN has a LONGER course to the neck than the right side. This is because it hooks under the left sixth arch artery which persists in extra-uterine life as the ductus arteriosus, a fibrous remnant which later fprms the ligamentum arteriosum.
ALSO NOTE that on the right side, the sixth arch artery disappears and the right RLN hooks under the right fourth arch artery which later becomes the right subclavian artery.