We evaluate the Brillouin frequency shift (BFS) determination error when using the Brillouin phase spectrum (BPS) instead of the Brillouin gain spectrum (BGS) in BOTDA setups. We compare the error obtained in the BFS determination in both cases, both with theoretical arguments and experimental data. In comparison to the gain, for an equal SNR and linewidth, the phase generally provides a better fit of the BFS for smaller frequency spans. This result opens a possible way to reduce the measurement time of certain BOTDA systems by using the phase feature.