Advanced soil constitutive models consist of multiple model parameters, which enable to capture the complex behaviour of soil, providing more accurate results. However, calibrating these numerous parameters is challenging which limits the widespread use of such models. To overcome such challenges, data assimilation methods such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) can be employed to improve the parameter estimates and model predictions. Although Bayesian methods employing such techniques have been applied in fields like health monitoring, signal processing, etc., its potential application in estimating parameters of critical state models is very limited. This paper presents a comparative analysis of MCMC and SMC for estimating the constitutive parameters of a critical-state based strain-hardening soil model. In this context, a stress-based single-element code of the model, designed to predict triaxial shearing response, has been integrated with the above two techniques for identifying the model parameters. To explore the intricacies involved in parameter estimation, experimental results of consolidated drained triaxial tests on loose Hostun sand for two different confining pressures are opted from the literature. Finally, a comparison between the two approaches has been presented to describe the effectiveness of these methods in estimating the constitutive model parameters.