  In the context of simulating precision laser interferometers, we compare via
several examples two wavefront decomposition methods: the Mode Expansion Method
(MEM) and the Gaussian beam decomposition (GBD) for their precision and
applicability. To judge the performance of these methods, we define different
types of errors and study their properties. We specify how the two methods can
be fairly compared and based on that, the quality of the MEM and GBD are
compared in several examples. We test here cases for which analytic results are
available, i.e., non-clipped circular and general astigmatic Gaussian beams, as
well as clipped circular Gaussian beams, in the near-, far-, and extreme
far-field of millions of kilometers occurring in space-gravitational wave
detectors. Additionally, we compare the methods for aberrated wavefronts and
the interaction with optical components by testing reflections from differently
curved mirrors. We find that both methods can be generally used for decomposing
non-Gaussian beams. However, which method is more accurate depends on the
optical system and simulation settings. In the given examples, the MEM more
accurately describes non-clipped Gaussian beams, while for clipped Gaussian
beams and the interaction with surfaces, the GBD is more precise.
