The radio astronomy community is rapidly adopting deep learning techniques to deal with the huge data volumes expected from the next generation of radio observatories. Bayesian neural networks (BNNs) provide a principled way to model uncertainty in the predictions made by such deep learning models and will play an important role in extracting well-calibrated uncertainty estimates on their outputs. In this work, we evaluate the performance of different BNNs against the following criteria: predictive performance, uncertainty calibration and distribution-shift detection for the radio galaxy classification problem.