  We compare three different models of rotating neutron star spacetimes: the
Hartle-Thorne (HT) slow-rotation approximation at second order in rotation, the
exact analytic vacuum solution of Manko et al. and a numerical solution of the
full Einstein equations. We integrate the HT structure equations for five
representative equations of state. Then we match the HT models to numerical
solutions of the Einstein equations, imposing that the mass and angular
momentum of the models be the same. We estimate the limits of validity of the
HT expansion computing relative errors in the spacetime's quadrupole moment Q
and in the ISCO radii. We find that ISCO radii computed in the HT approximation
are accurate to better than 1%, even for the fastest observed ms pulsar. At the
same rotational rates the accuracy on Q is of order 20%. In the second part of
the paper we focus on the exterior vacuum spacetimes. We introduce a physically
motivated `quasi-Kinnersley' Newman-Penrose frame. In this frame we evaluate
the speciality index S, a coordinate-independent quantity measuring the
deviation of each model from Petrov Type D. On the equatorial plane this
deviation is smaller than 5%, even for the fastest rotating models. Our main
conclusion is that the HT approximation is very reliable for most astrophysical
applications.
