In Gaussian case with uniform prior the result would be identical. The strength of Bayesian comes in the prior and information exchange between different components. When you have your model set up you can do all kinds of crazy thing, like taken into account the temporal information (eg trust more the measurements that are closer in time), spatial information (eg trust more the users that report closer measurement), weighted average (eg trust more the user with newer/better equipment) etc. All of these could be done by introducing additional structure and correlation into your model.