The result is identical, the understanding is different. I would suggest that the Bayesian perspective leads to insights like the UKF [1] which IME is all round

The result is identical, the understanding is different. I would suggest that the Bayesian perspective leads to insights like the UKF [1] which IME is all round much better than the apparently better known EKF for approximating non linear systems. [1] That is, it is generally easier to approximate a distribution than a non linear function.