The present work investigates and compares the computational performance of numerical techniques applied to the solution of algebraic and differential equations (DAEs) representing power systems and their components. Among the considered techniques, emphasis was given to the method known as Modified Extended Backward Differentiation Formulae (MEBDF), due to its numerical stability properties that conventional Backward Differentiation Formulae (BDF) methods do not have, and these properties may avoid numerical troubles during DAEs solution. The comparison is made through computational tests related to simulations of power system short- and long-term stability phenomena (transient angular stability and long-term voltage stability), using IEEE system-test. The main objective was to check the computational efficiency of these numerical techniques. The computational aspect is related to the simulation CPU time.