Background: Bayesian relaxed-clock dating has significantly influenced our understanding of the timeline of biotic evolution. This approach requires the use of priors on the branching process, yet little is known about their impact on divergence time estimates. We investigated the effect of branching priors using the iconic cycads. We conducted phylogenetic estimations for 237 cycad species using three genes and two calibration strategies incorporating up to six fossil constraints to (i) test the impact of two different branching process priors on age estimates, (ii) assess which branching prior better fits the data, (iii) investigate branching prior impacts on diversification analyses, and (iv) provide insights into the diversification history of cycads. Results: Using Bayes factors, we compared divergence time estimates and the inferred dynamics of diversification when using Yule versus birth-death priors. Bayes factors were calculated with marginal likelihood estimated with stepping-stone sampling. We found striking differences in age estimates and diversification dynamics depending on prior choice. Dating with the Yule prior suggested that extant cycad genera diversified in the Paleogene and with two diversification rate shifts. In contrast, dating with the birth-death prior yielded Neogene diversifications, and four rate shifts, one for each of the four richest genera. Nonetheless, dating with the two priors provided similar age estimates for the divergence of cycads from Ginkgo (Carboniferous) and their crown age (Permian). Of these, Bayes factors clearly supported the birth-death prior. Conclusions: These results suggest the choice of the branching process prior can have a drastic influence on our understanding of evolutionary radiations. Therefore, all dating analyses must involve a model selection process using Bayes factors to select between a Yule or birth-death prior, in particular on ancient clades with a potential pattern of high extinction. We also provide new insights into the history of cycad diversification because we found (i) periods of extinction along the long branches of the genera consistent with fossil data, and (ii) high diversification rates within the Miocene genus radiations.