The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled-cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. We consider the infinite-order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects. We have also calculated the spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2, and the binding energies of Be3, Be4, Mg3, and Mg4 using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as nondynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical system under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant, both QCI and CC give very similar results.