The third flight of the high-altitude balloon-borne ANtarctic Impulsive Transient Antenna (ANITA III) planned for December 2014 will be optimized for the measurement of impulsive radio signals from Ultra-High Energy Cosmic Rays (UHE CR), i.e. charged particles with energies above 1019 eV, in addition to the high-energy neutrinos ANITA was originally designed for. The event reconstruction algorithm for UHE CR relies on the detection of radio emissions in the frequency range 200-1200 MHz (RF) produced by the charged component of extensive air showers initiated by these particles. UHE CR energy reconstruction methods are based on Monte Carlo simulations of the RF emission from these showers and on modeling of the detector response to such emission. A full UHE CR energy reconstruction algorithm for ANITA III involving detector modeling is a work in progress. In this paper, we evaluate expected systematic uncertainties in ANITA reconstructed energies only due to differences in the RF emission models by comparing outputs of two RF simulation packages, CoREAS and ZHAireS, and propagating the differences in the outputs through an energy reconstruction method using an idealized detector model.