We investigate similarities and differences between natural and simulated slow earthquakes using nonlinear dynamical system tools. We use spatio-temporal slip potency rate data derived from Global Navigation Satellite System (GNSS) position time series in the Cascadia subduction zone and numerical simulations intended to reproduce their pulse-like behavior and scaling laws. We provide metrics to evaluate the accuracy of simulations in mimicking slow earthquake dynamics. We investigate the influence of spatio-temporal coarsening as well as observational noise. Despite the use of many degrees of freedom, numerical simulations display a surprisingly low average dimension, akin to natural slow earthquakes. Instantaneous dynamical indices can reach large values ($>10$) instead, and differences persist between numerical simulations and natural observations. We propose to use the suggested metrics as an additional tool to narrow the divergence between slow earthquake observations and dynamical simulations.