In comparison with the minimum energy criterion as an indicator of the most stable state, the minimum polarizability and maximum hardness principles have been examined to describe the relative stability of various isomers of nine gaseous all-metal clusters M4X(-) (Cu4Na-, Cu4Li-, Al4Cu-, Ag4Li-, Au4Li-, Ag4Na-, Au4Na-, Al4Ag-, Al4Au-) on the basis of MP2 calculations. In these species, there are two lowest energy isomers with near isoenergy that sometimes make it very difficult to determine which of them is more stable when we depend only on the minimum energy criterion. According to the minimum polarizability principle, however, the square-pyramidal structure is always more stable than the planar isomer at various computational levels, which was also confirmed by the results from the minimum energy principle that sometimes requires higher computational precision. Thus, there is an indication that, at least for our present cluster system, the minimum polarizability principle is less dependent on the computational levels compared to the minimum energy principle.