Ensemble-based data assimilation systems based on linear estimation techniques have generally divided into two classes: stochastic filters and deterministic filters. These Monte Carlo methods are useful as a way to estimate flow-dependent error structures. They are also useful as a means to make and interpret probabilistic forecasts, where one relies on each ensemble member being statistically indistinguishable from truth, i.e. the ensemble and truth share the same probability density function. We want to gauge if both filter classes are capable of producing correct probabilistic forecasts in varying regimes of error growth. To this, we inspect the update process of the different filter classes in a perfect model scenario using a two-dimensional dynamical system, the Ikeda map. We offer a geometric interpretation of how their behavior changes as nonlinear error growth becomes appreciable. We link this interpretation to ensemble rank histogram assessment. We conclude that both filters perform as expected in a linear regime, but that stochastic filters can better withstand regimes with nonlinear error growth.