It is interesting to note that a very hard material such as diamond and a relatively soft material such as a polymer both contain covalent bonding.
The large differences in properties can be explained by considering the rigid 3D structure of diamond. Polymers have a less 3D covalently bonded structure. Rather, they have long chain molecules that are typically held together with either secondary bonds or a limited amount of covalent bonding (cross-linking).
Thus it is important, when considering material properties, to not only look at the bonding within the molecules but also the bonds that keep the molecules together.
It is possible to have interatomic bonds that are partially ionic and partially covalent. In fact, very few compounds show either purely ionic or purely covalent bonding.
The wider the separation on the periodic table, the more ionic in nature the bonding. The increased tendency for ionic bonding is a result of the increase in electronegativity between elements. The closer the elements, the more covalent in nature the bonding.