Numerical simulations have been the primary tool to study compact binary coalescences in the last two decades, supplying a wealth of information. Depending primarily on the total mass of the binary, a possible outcome of a binary neutron star merger is a long-lived (with a lifetime > 10ms) compact remnant supported by differential rotation. In this work, we present equilibrium sequences of rotating relativistic stars, constructed with a new differential rotation law that was proposed by Uryu et al. (2017). We choose rotational parameters motivated by numerical simulations of binary neutron star merger remnants, but otherwise adopt a cold, relativistic N=1 polytropic equation of state, in order to perform a detailed comparison to published equilibrium sequences that used the Komatsu, Eriguchi and Hachisu (1989) differential rotation law. We find a small influence of the choice of rotation law on the mass of the equilibrium models and a somewhat larger influence on their radius. The versatility of the new rotation law allows us to construct models that have a similar rotational profile and axis ratio as observed for merger remnants, while at the same time being quasi-spherical. While our models are highly accurate solutions of the fully general relativistic structure equations, we demonstrate that for models relevant to merger remnants the IWM-CFC approximation still maintains an acceptable accuracy.