Before revision:  For both models, we devise scalable and gradient-free Bayes estimators. We compare MNP, MNR and Gen-MNR in a simulation study and a case study on transport mode choice behaviour .
After revision:  For both models, we derive efficient Gibbs sampling schemes, which also allow for a straightforward inclusion of random parameters. In a simulation study, we illustrate the excellent finite sample properties of the proposed Bayes estimators and show that MNR and Gen-MNR in a simulation study and a case study on transport mode choice behaviour .