They currently operate on disjoint sets of roads, so they can only be roughly compared, and in rough comparison they do not behave differently. Of course if operated on the exact same road (which, again, is currently impossible) their actions would not be the same in every detail, just as different humans or even the same human driving the same road multiple times wouldn't. But that doesn't mean that there's necessarily any consistent difference that would enable a driver to use the information of which one is active to improve their predictions of the car's behavior.
