Here we present and compare functional and spatiotemporal (Sp.T.) kriging approaches to predict spatial functional random processes, which can also be viewed as Sp.T. random processes. Comparisons are focused on Sp.T. kriging versus ordinary kriging for functional data (OKFD), since more flexible functional kriging approaches like pointwise functional kriging and functional kriging total model coincide with OKFD in several situations. Prediction performance is evaluated via functional cross-validation on simulated data as well as on a Canadian weather data set. The two kriging approaches perform in many cases rather equal for stationary Sp.T. processes. For nonstationary Sp.T. processes, OKFD performs better than Sp.T. kriging. The computational time for OKFD is considerably lower compared to those for the Sp.T. kriging methods.