It is possible that adsorption data fits both kinetic models. Results may be validated based a combination of statistical tool such as value of correlation coefficient (R2), chi square, RMSE.
You may refer to
Characterization, kinetics and thermodynamics of Ag(I) sorption using novel sorbent: Dry wheatgrass
The adsorption data can fit the pseudo-first or pseudo-second order model. To determine the best model, it suffices to make a comparison between the statistical criteria (R2, AARD, RMSE, SSE, SSR) of the tested models .