Nagato would win.
Normal techniques wouldnt work on the 3rd but nagato's technqiues are all derived from his rennigan and they are all insane. Tbh we didnt see much of what the rennigan can do, but from what weve seen, its safe to give this fight to nagato.
Taijutsu wouldnt work and neither will any of the raikage ninjutsu. Either by him repeling with shira tensei or absoring his techniques. Nagato has many ways he can defeat the raikage and i cannot come up with ways in which the raikage could defeat nagato