We investigate five different models for the dark matter (DM) halo bias, that is, the ratio of the fluctuations of mass tracers to those of the underlying mass, by comparing their cosmological evolution using optical quasar (QSO) and galaxy bias data at different redshifts, consistently scaled to the WMAP7 cosmology. Under the assumption that each halo hosts one extragalactic mass tracer, we use a χ²-minimization procedure to determine the free parameters of the bias models as well as to statistically quantify their ability to represent the observational data. Using the Akaike information criterion we find that the model that represents best the observational data is the Basilakos & Plionis model with the tracer merger extension. The only other statistically equivalent model, as indicated by the same criterion, is the Tinker et al model. Finally, we find an average, over the different models, DM halo mass that hosts optical QSOs of Mₕ ≃ 2.7 (±0.6) × 10¹² h⁻¹MꙨ, while the corresponding value for optical galaxies is Mₕ≃ 6.3 (±2.1) × 10¹¹ h⁻¹MꙨ.