[en] We assess the accuracy and limitations of two analytic models of the tokamak bootstrap current: (1) the well-known Sauter model (1999 Phys. Plasmas 6 2834, 2002 Phys. Plasmas 9 5140) and (2) a recent modification of the Sauter model by Koh et al (2012 Phys. Plasmas 19 072505). For this study, we use simulations from the first-principles kinetic code NEO as the baseline to which the models are compared. Tests are performed using both theoretical parameter scans as well as core-to-edge scans of real DIII-D and NSTX plasma profiles. The effects of extreme aspect ratio, large impurity fraction, energetic particles, and high collisionality are studied. In particular, the error in neglecting cross-species collisional coupling—an approximation inherent to both analytic models—is quantified. Furthermore, the implications of the corrections from kinetic NEO simulations on MHD equilibrium reconstructions is studied via integrated modeling with kinetic EFIT. (paper)