  We present the first direct comparison of codes based on two different
numerical methods for constructing rapidly rotating relativistic stars. A code
based on the Komatsu-Eriguchi-Hachisu (KEH) method (Komatsu et al. 1989),
written by Stergioulas, is compared to the Butterworth-Ipser code (BI), as
modified by Friedman, Ipser and Parker. We compare models obtained by each
method and evaluate the accuracy and efficiency of the two codes. The agreement
is surprisingly good. A relatively large discrepancy recently reported
(Eriguchi et al. 1994) is found to arise from the use of two different versions
of the equation of state. We find, for a given equation of state, that
equilibrium models with maximum values of mass, baryon mass, and angular
momentum are (generically) all distinct and either all unstable to collapse or
are all stable. Our implementation of the KEH method will be available as a
public domain program for interested users.
