Seismic fragility curves are key quantities of the Seismic Probabilistic Risk Assessment studies carried out on industrial facilities. They express the probability of failure of a mechanical structure conditional to a scalar value derived from the seismic ground motion called Intensity Measure (IM). Estimating such curves is a daunting task because for most structures of interest few data are available. For this reason, some methods of the literature rely on the use of the parametric log-normal model coupled with Bayesian approaches for parameter estimation. We are interested in this work in binary datasets (failure or not failure) and we investigate the influence of the choice of the prior and of the IM – Peak Ground Acceleration vs. Pseudo Spectral Acceleration – on the convergence of the estimates for a given seismic scenario. We show that Bayesian fragility curve estimation results based on Jeffreys’ prior outperform the ones based on classical priors whatever the IM. We also show that, when an IM is more correlated to the structural response, the differences between the results obtained with the different priors are less marked. They testify to the fact that an IM more correlated to the response of the structure induces a lower variability of the estimate of the median of the log-normal model. This is not the case for the log standard deviation whose estimate is affected by samples which are more degenerate with this kind of IM, namely which are partitioned into two disjoint subsets when classified according to IM values: the subset for which there is no failure and the other one for which there is failure, these two subsets possibly being present in the same sample or separately. Such degeneracy affects all methods to varying degrees, but with Jeffreys’ prior the results are clearly better, attesting to its robustness against such inevitable situations in practice.