Recently, time-dependent density-functional (TDDFT) methods have been developed for determining the energies of molecular excited states. This, along with the somewhat similar equations-of-motion coupled-cluster (EOM-CCSD) methods, offer advantages of speed, reliability, and often accuracy over alternate complete-active-space self-consistent-field (CASSCF) based approaches, with the disadvantages associated with being essentially "single-reference" calculations. We compare results obtained using both approaches for the (1)Sigma(g)(+) (ground) and (3)Sigma(u)(-) (first excited) states of the simplest molecule, H-2. For the excited state of this two-electron system, EOM-CCSD is equivalent to full configuration interaction, while results obtained using TDDFT are good at short bond lengths but become quite poor as the bond is stretched from its equilibrium length. The poor TDDFT result is attributed to the fact that the spin-restricted Kohn-Sham (RKS) method used to generate the ground-state density is not size consistent. We suggest that TDDFT calculations based on spin-unrestricted Kohn-Sham (UKS) calculations should provide better descriptions of molecular excited states than do current RKS-based methods, spin-contamination effects notwithstanding.