Both of these design methods produce runs with three levels for each factor. The full factorial, of course, produces all combinations of factor levels. The response surface methods (e.g., Box-Behnken or Box-Wilson) do not. The Box-Behken is more economical for the typical optimization situation involving only a few factors (after screening) but does not share any runs with the two-level screening designs. The Box-Wilson designs are also called the central composite designs because they are composed of a two-level factorial design, axial points, and center points.
You can probably do better (smaller prediction standard errors from fewer runs) with a custom design for I-optimality than either of the older response surface methods.
I recommend:
