The fusion of camera sensor and inertial data is a leading method for ego-motion tracking in autonomous and smart devices. State estimation techniques that rely on non-linear filtering are a strong paradigm for solving the associated information fusion task. The de facto inference method in this space is the celebrated extended Kalman filter (EKF), which relies on first-order linearizations of both the dynamical and measurement model. This paper takes a critical look at the practical implications and limitations posed by the EKF, especially under faulty visual feature associations and the presence of strong confounding noise. As an alternative, we revisit the assumed density formulation of Bayesian filtering and employ a moment matching (unscented Kalman filtering) approach to both visual-inertial odometry and visual SLAM. Our results highlight important aspects in robustness both in dynamics propagation and visual measurement updates, and we show state-of-the-art results on EuRoC MAV drone data benchmark.