A roadie coil produces consistent loops, which are large-radius bends, aka gentle bends. This is what you want for electrical cable, especially high-quality expensive cables you want to last a long time. Tight-radius bends, aka kinks, can cause premature failure.
Folding is fine if the cord is extremely flexible, or for rope.
Folding done right produces no twists at all about the axis of the line, which is ideal. That’s why it is the preferred method for packaging rock climbing ropes. The roadie coil produces alternating twists that mostly cancel each other out once it is fully uncoiled.