While software developers may give the impression that CBC conjoint is clearly superior, academic research is far less clear; both in terms of parameter estimates and in terms of predictive validity.
In terms of parameters, Karniouchina et al. (2008) found only slight differences between parameter estimates – implying similar estimates of attribute importance. Indeed Karniouchina et al. (2008) concluded "This study, along with the other articles in this research stream, strongly suggests that in traditional conjoint tasks, the parameter estimates produced by RB and CB conjoint models are likely to be quite similar."
In terms of predictive validity, a study by Elrod et. al (1992) of rental apartments demonstrated that CVA and CBC conjoint produced similar results, "both approaches predict holdout shares well…".
Karniouchina et al. (2008) in a study of laptops found that 'hit rates' (percentage of times the hold-out choice matches predicted choice) at the individual level were better for a more complex form of CBC called hierarchical bayes (HB CBC); but no significant difference was found with segment level hit rates or aggregate level hit rates. In terms of predicted share of choice "no significant differences between the individual- or segment-level RB [i.e. CVA conjoint] and CB [i.e. CBC conjoint] models " were found, while there was a significant difference at the aggregate level. A peculiarity of this study should be pointed out, in that HB was used for the individual level parameter estimates for CVA.
While hardly an exhaustive examination of academic studies on this topic, these few studies should make it clear that there is noting near a consensus on CBC being superior in predicting hold outs (preference share at the aggregate level). If the aim of your study is to predict market share, rather than preference share, then any differences in performance are even less relevant. When you consider that conjoint analysis is an incomplete model, in the sense that it ignores the promotional and accessibility aspects of the marketing mix and has modest external validity (without calibrating for these missing variables) it is doubtful any slight differences between CVA and CBC in terms of hold-out predictions matters much in practice.