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). Their implementation of the nested fixed point algorithm used successive approximations to solve the inner fixed point problem (NFXP-SA). 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 are similar in speed and numerical performance when the more efficient NFXP-NK variant is used.