The local particle filter (LPF) and the local nonlinear ensemble transform filter (LNETF) are two moment-matching nonlinear filters to approximate the classical particle filter (PF). They adopt different strategies to alleviate filter degeneracy. LPF and LNETF localize observational impact but use different localization functions. They assimilate observations in a partially sequential and a simultaneous manner, respectively. In addition, LPF applies the resampling step, whereas LNETF applies the deterministic square root transformation to update particles. Both methods preserve the posterior mean and variance of the PF. LNETF additionally preserves the posterior correlation of the PF for state variables within a local volume. These differences lead to their differing performance in filter stability and posterior moment estimation. LPF and LNETF are systematically compared and analyzed here through a set of experiments with a Lorenz model. Strategies to improve the LNETF are proposed. The original LNETF is inferior to the original LPF in filter stability and analysis accuracy, particularly for small particle numbers. This is attributed to both the localization function and particle update differences. The LNETF localization function imposes a stronger observation impact than the LPF for remote grids and thus is more susceptible to filter degeneracy. The LNETF update causes an overall narrower range of posteriors that excludes true states more frequently. After applying the same localization function as the LPF and additional posterior inflation to the LNETF, the two filters reach similar filter stability and analysis accuracy for all particle numbers. The improved LNETF shows more accurate posterior probability distribution but slightly worse spatial correlation of posteriors than the LPF.