We revisit the comparison of mathematical programming with equilibrium constraints (MPEC) and nested fixed point (NFXP) algorithms for estimating structural dynamic models by Su and Judd (SJ, 2012). They used an inefficient version of the nested fixed point algorithm that relies on successive approximations. We re-do their comparison using the more efficient version of NFXP proposed by Rust (1987), which combines successive approximations and Newton-Kantorovich iterations to solve the fixed point problem (NFXP-NK). We show that MPEC and NFXP-NK are similar in performance when the sample size is relatively small. However, in problems with larger sample sizes, NFXP-NK outperforms MPEC by a significant margin.