The spin nonadapted or partially spin adapted spin orbital multireference (MR) state-universal (SU) or Hilbert space coupled cluster (CC) method is analyzed from the viewpoint of possible spin symmetry breaking or spin contamination and contrasted with the recently introduced state specific (SS), automatically spin adapted, spin-free unitary group based CC method. It is shown that the partial spin-adaptation of the two-determinantal MR SUCC approach can only be effective if the complementary singlet and tripler states have a similar structure in the sense that their weights at corresponding singlet and triplet configurations, having the same orbital occupancies, are identical or nearly identical. The performance of both SS and SU CC methods, and of corresponding CI method (all truncated at the double excitation level) for the lowest lying open-shell singlet and triplet states of the H4 and H8 model systems was examined, showing the superiority of the unitary group based CC approach in all studied aspects.