In this article we reconsider the discussion of the magnetic measurements for the two novel polyoxotungstates, (n-BuNH3)(12)[(CuCl)(6)(AsW9O33)2]center dot 6H(2)O and (n-BuNH3)(12)[(MnCl)(6)(SbW9O33)(2)]center dot 6H(2)O, which have been synthesized and characterized by Yamase et al. (Inorg.Chem. 2006, 45, 7698). Analysis of the magnetic susceptibility and magnetization for Cu-6(12+) and Mn-6(12+) hexagons based on the exact diagonalization of isotropic exchange Hamiltonian shows that the best-fit first-neighbor coupling parameters are J = 35 and 0.55 cm(-1), respectively, while the second-neighbor interactions are very small. These values exceed considerably those obtained by Yamase et al. (J = 8.82 and 0.14 cm(-1)) on the basis of the Kambe-Van Vleck formula that is inappropriate for six-membered rings. We also got perfect fits to the experimental data for the field dependence of magnetization at 1.8 K. The results imply the importance of axial anisotropy, which is shown to be especially pronounced for the Mn-6(12+) cluster. We discuss also the symmetry assignments of exchange multiplets to the exact S Gamma terms (full spin, S, and irreducible representation, Gamma, of the point group) and correlate the results with the selection rules for the anisotropic magnetic contributions. The antisymmetric exchange is shown to appear in orbitally degenerate multiplets as a first-order perturbation and gives rise to an easy axis of magnetization along the C-6 axis. Evaluation of the Zeeman levels shows that the field applied in the plane of the hexagon fully reduces the effect of the antisymmetric exchange.