The article is devoted to the theoretical study of the four-site cells as the basic units in the architecture of quantum-dot or molecular cellular automata. The functional characteristics of two possible compositions of square cells for quantum cellular automata are compared. We analyze the properties of the tetrameric cells composed of two isolated one-electron dimers (half-cells) and the cells based on the bi-electron tetramers (full cells). The inter-site Coulomb interactions and the electron transfer processes are taken into account as well as the external field of the neighboring cell. The difference in the transfer pathways is shown to result in a more abrupt nonlinear cell-cell response function for the double-dimer arrangement of the charge containers. This result shows that the double-dimeric cell is preferable to design quantum cellular automata devices.