Wave excitation force (torque) estimators, vital in wave energy systems, generally combine the nominal representation of a wave energy converter (WEC) with an excitation force (perturbation) model. Thus, this model-based estimation approach, grounded in the internal model principle, often employs two perturbation models: (i) the harmonic oscillator structure, prevalent in literature, assuming sinusoidal signals; and (ii) the integrator (random walk) scheme, assuming unit step-like signals. These models comprehensively represent a specific family of estimators, as discussed in this study. However, both models may struggle to capture the irregular (stochastic) nature of ocean waves. This study challenges the prevailing assumption that the harmonic oscillator structure, selected for its resemblance to ocean wave oscillations, is inherently the optimal choice. This study provides a rigorous discussion on convergence conditions. Thus, is shown that, while the harmonic oscillator can be highly effective under specific conditions, the random walk structure, despite its simplicity, can surpass the performance of the harmonic oscillator scheme. Formal proofs support this argument, emphasising the effectiveness of the harmonic oscillator can be guaranteed with periodic signals.