Parabolic equation (PE) based methods are widely used in outdoor acoustics because they can solve acoustic propagation problems above a mixed ground in a refractive and scattering atmosphere. However, recent research has shown phase error due to the effective sound speed approximation (ESSA). To overcome these limitations, a new PE formulation derived without the ESSA has been proposed recently. We investigate the impact of such phase error on wind turbine noise modeling, as the classical wide-angle parabolic equation (WAPE) with ESSA is widely used in the research community. We propose a comparison between the classical WAPE with ESSA and the new WAPE derived without the ESSA in the context of wind turbine noise. We highlight large phase error (several dB) on monochromatic calculations with a point source. Using an extended sound source representative of a wind turbine, we show small phase error (<1 dB) in a wind turbine noise context where sound level variability far from the source is of several dB. The validity of previous works using WAPE with ESSA is, thus, not questioned, although we do recommend the use of the new WAPE derived without the ESSA to accurately model the effect of wind speed on sound propagation.