Difficult to know, simply because the courts are not as much of a concern to authors discussing the Principate as the Republic. By and large, the only cases really discussed in historical sources tend to be political cases within Rome itself, and these were the exact sorts of cases that came under the emperor's direct oversight. So we have very little idea about the effects of the transition from Republic to Principate, except that administration in governance in general became more localized. Whether it was less corrupt or not is impossible to say for certain.