For some years, choice-based conjoint analysis (CBC) has demonstrated its superiority over other preference measurement alternatives. So, e.g., in a recent study on German and Polish cola consumers, the superiority of CBC over traditional conjoint analysis (TCA) was striking. As one reason for this superiority, the usage of hierarchical Bayes for CBC parameter estimation was mentioned (CBC/HB). This paper clarifies whether this really makes the difference: Hierarchical Bayes is also used for TCA parameter estimation (TCA/HB). The application to the above mentioned data shows, that this improves the predictive validity compared to TCA but is still inferior to CBC/HB in “high data quality cases". However, in “low data quality cases" TCA/HB is superior to CBC/HB.