There are typically two different situations:
1) Control lines that runs through blocks, with a gear ratio (e.g. 1:4) damping the effect of rope tension and elongation on sail trim. Here good grip, some flexibility are most important. The outhaul needs to be easy to manually handle.
2) Lines in systems, often taking the total load (so without gear). These lines should have higher strength and low elongation to ensure good a sail trim. The sail stays flat with increasing winds. Recreational sailors can use polyester.