Both these deckchair fabrics are hard wearing, but the polycotton just has the edge in terms of longevity. The polycotton fabric is made up of a polythene warp and a cotton weft, which gives it a nice cotton feel but with the added strength provided by a synthetic fibre. The green cotton fabric is also hard wearing, but being pure cotton it is more likely to rot or tear if left wet.
That being said all deckchairs are best taken indoors after use and should be kept dry and stored somewhere well ventilated. They are designed for use on dry days and not to be left out in the rain.