Finite element (FE) model updating is extensively employed in many applications of various engineering branches for damage detection purposes. An FE model is expected to reflect the properties of actual structures. However, it is almost impossible for an FE model to carry the properties of the real-life structure. As a result, differences exist between analytical models and actual structures. The aim of model updating is to minimize these differences as much as possible. In model updating procedures, there are inevitable uncertainties due to inevitable measurement noise and modelling errors. Therefore, model updating and damage detection process should be performed in a probabilistic way instead of a deterministic one. To this end, Bayesian model updating methods have gained much attention in the literature to account for the uncertainties of the parameters to be updated. Among these methods, those that use the concept of system modes have gained much more attention since it enables researchers to account for modelling error uncertainties and to avoid mode matching problem. For those methods, discrepancies between system modes and measured modes are considered and system modes are updated to obtain those that best fit the measured modes. Further, system modes are connected to the FE model via eigenvalue equations. In this study, a two-stage Bayesian model updating method which utilizes the concept of system modes has been firstly reformulated to compare three different assumptions on the modelling error variance of eigenvalue equations. Results reveal that the Bayesian model updating formulations that use the system modes concept give unreasonably too small posterior uncertainties for the updated parameters. This makes the probabilistic approach questionable since getting such small uncertainties may almost be equivalent to a deterministic approach. To increase the posterior uncertainty levels to more reasonable levels, a two-stage sensitivity-based Bayesian model updating methodology is proposed in this study. The results show that the proposed method successfully improves the updating results and increases the posterior uncertainties to more realistic levels.