The prologue of the reboot involves the game taking control of your car in order to stop it. This is a subtle way of showing that your car ran out of fuel and stopped, allowing you to be easily caught. This doesn't happen in the Duke/Tex/Death Matches because, by that point, you've got a better car with better fueling mechanisms and, of course, lots of armor and guns. You can even say that, by the time you got rid of the Adversary, you already have a Golden Shrieker, thus a way much better car to avoid and resist the police, which may be the reason they stopped caring about you.
