This contribution reports a comparative analysis of two methodologies for the periodic steady-state solution of linear and nonlinear electric networks in time-domain (TD), based on the state-space model (SSM) and companion-circuit analysis (CCA), respectively. Newton methods based on a conventional Numerical Differentiation (ND) and Enhanced Numerical Differentiation (END) process, respectively, are used. The application of the SSM and CCA methods is done using a brute force (BF) procedure and the application of advanced numerical techniques (ANT) through the forward Euler (FE) and Trapezoidal Rule (TR) numerical integration, respectively. Related analysis show comparisons of each case study in terms of efficiency, speed, computer effort and accuracy between the combination of SSM, CCA and Newton methods, e.g. SSM-ND, SSM-END, CCA-ND and CCA-END, respectively. In particular, the analysis is shown in terms of time-steps per period, CPU processing time and a computer platform used are shown. The results obtained from the reported case studies are validated against the Power Systems Computer Aided Design/Electromagnetic Transients Program including Direct Current (PSCAD/EMTDC®) response, widely accepted by the power industry.