Hybrid choice models are a generalisation of standard discrete choice models where different expanded models are considered simultaneously. Using a virtual case of travel mode choice, in this paper we discuss the specification, estimation, and point estimate analysis of a hybrid choice model that allows us to include qualitative attributes in a standard discrete choice setting in a way that avoids problems of inconsistency. In particular, we set up a Monte Carlo experiment where we compare the point estimation results of two alternative methods of estimation, namely frequentist full information simulated maximum likelihood and Bayesian Metropolis Hastings-within-Gibbs sampling. Even though the two estimation methods we analyse are based on different philosophies, both the frequentist and Bayesian methods provide estimators that are asymptotically equivalent. Our results show that both methods are feasible and offer comparable results with a large enough sample size. However, the Bayesian point estimates outperform maximum likelihood in terms of accuracy, statistical significance, and efficiency when the sample size is low.