Since the early 70's the Split-Step Fourier Method (SS/FM) has been widely adopted for the optics community. In this work, in order to get insights for more complex nonlinear scalar or vectorial simulations, which could include simultaneous spatial and temporal soliton analysis, a comparison among the most common two SbS/FEM algorithms, our FE scheme and the well known SS/FM has been performed. To reach this goal, as a model, the dimensionless nonlinear Schroedinger (NLS) equation, associated to the Kerr nonlinearity type, has been adopted.