Both tight binding and nearly free electron models are ways to determine band structure of solids. They are complementary to each other. Nearly free electron model applies more to weak periodic potentials and tight binding is more representative of strong potentials. Or more accurately, nearly free electron starts in the plane wave limit of completely free electrons and adds potentials weakly, whereas tightbinding starts in the limit of electrons on atomic orbitals and adds hopping between orbitals weakly. As is often the case, the truth lies between the two limits. Both approaches have the advantage of being extremely simple to work with whereas really accurate band structure calculations must be put on a computer to solve and it is hard to develop any clear intuition for what is going on.