Actually they are both prone to deterioration. The casings when made of natural fibers are prone to dry rot(actually a term for cellulose based materials like cotton) but since most of the casings are made of synthetics they no longer have dry rot issues. The rubber can break down due to UV radiation, Ozone and petroleum based products. Moisture is no longer an issue since casings are now synthetic

edit: Ozone will not effect synthetic rubbers, only gum rubber(natural rubber) is effected this way