It really really depends. At the end of the day your safety and the safety of others is what is important. If the Offender gets away so be it, but you do no one any good if you die in a wreck. Essentially I just drive the same way I drive to any emergency, except I try to keep my eyes on the vehicle obviously.
Training (EVOC and more advanced courses), experience in the vehicle at high speeds simply responding to calls, and inexperienced drivers who flee - all help officers stay close to the fleeing vehicle. Air support, tire deflation devices, PIT training, decent radios and restraint all play a part as well.
Pursuit driving including vehicle dynamics and weight shifts, braking techniques, knowing influences of terrain/weather/roadway composition including drag factors/knowing traffic patterns-typical driver responses all give a well trained and practiced officer an advantage.
Very carefully.