Stretchy sailcloth can be used to make sails that flatten when the pressure increases. For this reason, they are useful in a wider range of wind speeds and replace more then one rigid sails, which are more wind-speed specific.

A stretchy sail is slower then the two or three rigid sails it replaces - if you can always have the proper rigid sail up. However, the wind speed may be very variable and eventually you'll be caught with the wrong sail up. Also, in these conditions you'll have to change sails more frequently, making the stretchy sail a better choice.

Summary: a properly designed stretchy sail (one that flattens with higher pressure) is an advantage in highly variable conditions.

Durability is a separate issue.