It is demonstrated that among various possible isomers of all-metal aromatic compounds such as Al-4(2-) and their complexes the most stable isomer with the minimum energy is the hardest and the least polarizable. A similar situation is observed for different isomers of all-metal antiaromatic compounds such as Al-4(4-) and their complexes. It is shown that linear Al-4(4-) is energetically more stable than its cyclic isomer. The reaction energies associated with the complexation processes highlight the stability of those complexes. The difference in energy, hardness, and polarizability between a cyclic molecule and its linear counterpart convincingly shows that an aromatic molecule exhibits negative changes in energy and polarizability but positive changes in hardness as expected from the principles of minimum energy, minimum polarizability, and maximum hardness. Although the aromaticity of Al-4(2-) is unequivocally established through this study, the antiaromaticity picture in the case of Al-4(4-) is shown to be poorly understood; however, the present analysis sheds light on this controversy.