This work regards the analysis of the seismic response of bridges isolated with single concave friction pendulum devices, including or neglecting the presence of the rigid abutment. Two six degree-of-freedom models are considered for the two cases, in order to represent the response of the elastic reinforced concrete pier and of the infinitely rigid reinforced concrete deck. The behavior of the friction pendulum isolators accounts for the non-linear dependency of the friction coefficient on the sliding velocity. The comparison is carried out by including the aleatory uncertainty in the seismic input (i.e., accounting for different natural records with different characteristics) and by varying the modelling properties within a parametric analysis. Finally, by solving the equations of motion in nondimensional form, the difference between the two models are deepened in terms of influence of the seismic isolation.