In order to obtain energy and momentum (due to matter and fields including gravitation) distributions of the Gibbons-Maeda dilaton spacetime, we use the Moller energy-momentum prescription both in Einstein"s theory of general relativity and teleparallel gravity. We find the same energy distribution for a given metric in both of these different gravitation theories. Under two limits, we also calculate energy associated with two other models such as the Garfinkle-Horowitz-Strominger dilaton spacetime and the Reissner-Nordstrom spacetime. The energy obtained is also independent of the teleparallel dimensionless coupling constant, which means that it is valid in any teleparallel model. Our result also sustains (a) the importance of the energy-momentum definitions in the evaluation of the energy distribution for a given spacetime and (b) the viewpoint of Lessner that the Moller energy-momentum complex is a powerful concept of energy and momentum (c) the hypothesis of Vagenas that there is a connection between the coefficients of the energy-momentum expression of Einstein and those of Moller.