We calculate the ionization potential and electron affinity of 1D Hubbard chains with a variety of different site energies from two perspectives: (i) the physics-based GW approximation and (ii) the chemistry-based configuration interaction (CI) approach. Results obtained from all methods are compared against the exact values for three classes of systems: metallic, impurity doped, and molecular (semiconducting/insulating) systems. Although all methods are reasonably accurate for weakly correlated systems, the GW method is significantly more reliable for strongly correlated systems with little disorder unless explicit double excitations are included in the CI. In principle, our results should offer some intuition about the choice of methodologies as well as state references for different classes of physical systems.