We evaluate the Brillouin frequency shift (BFS) determination error when utilizing the Brillouin phase spectrum (BPS) instead of the Brillouin gain spectrum (BGS) in BOTDA systems. Systems based on the BPS perform the determination of the BFS through a linear fit around the zero de-phase frequency region. An analytical expression of the error obtained in the BFS determination as a function of the different experimental parameters is provided and experimentally validated. The experimental results show a good agreement with the theoretical predictions as a function of the number of sampling points, signal-to-noise ratio (SNR) and Brillouin spectral linewidth. For an equal SNR and linewidth, the phase response only provides a better BFS estimation than the gain response when the fit is performed over a restricted frequency range around the center of the spectral profile. This may reduce the measurement time of specific BOTDA systems requiring a narrow frequency scanning. When the frequency scan covers most of the Brillouin spectral profile, gain and phase responses give very similar estimations of the BFS and the BPS offers no crucial benefit.