The effects of reactant ion rotational excitation on the exothermic proton-transfer reactions of HBr(+)((2)Π(1/2)) and DBr(+)((2)Π(1/2)), respectively, with CO(2) were studied in a guided ion beam apparatus. Cross sections are presented for collision energies in the center of mass system E(c.m.) in the range of 0.23 to 1.90 eV. The HBr(+)/DBr(+) ions were prepared in a state-selective manner by resonance enhanced multiphoton ionization. The mean rotational energy was varied from 3.4 to 46.8 meV for HBr(+)((2)Π(1/2)) and from 1.8 to 40.9 meV for DBr(+)((2)Π(1/2)). Both reactions studied are inhibited by collision energy, as expected for exothermic reactions. For all collision energies considered, the cross section decreases with increasing rotational energy of the ion, but the degree of the rotational dependence differs depending on the collision energy. For E(c.m.) = 0.31 eV, the cross sections of the deuteron transfer are significantly larger than those of the proton transfer. For higher E(c.m.) they differ very little. The current results for the exothermic proton transfer are systematically compared to previously published data for the endothermic proton transfer starting from HBr(+)((2)Π(3/2)) [L. Paetow et al., J. Chem. Phys. 132, 174305 (2010)]. Additional new data regarding the latter reaction are presented to further confirm the conclusions. The dependences on rotational excitation found cannot be explained by the corresponding change in the total energy of the system. For both the endothermic and the exothermic reaction, the cross section is maximized for the smallest rotational energy, at least well above the threshold.