In the case of fixed bases, there will be bending moments at the column bases, which have to be accounted for in the foundation design. In the case of hinged bases, there will be no bending moments transmitted to the foundations, whose design will be simpler (but higher moments will develop at the beam column junctions, compared to the fixed base case).
Whether it is appropriate to model the base as hinged or fixed depends on the soil conditions and type of foundations! It would be inappropriate, for example to assume hinged supports when the foundation is resting on hard strata. But if the foundation is on relatively soft strata, even a small rotation at the base can release any assumed fixed end moment...