As the years have gone by the police package items have gotten better. Better engine and a/c cooling, better special seats so your gun doesn't eat into the foam, oil coolers, pursuit rated tires, huge alternators, etc. Slightly higher idle speed in some cases, some react to driver input and go into 'pursuit mode' by raising the shift points, holding the gear you are in longer. The newer Explorers have this feature and it is very noticeable. Check out the brakes on a new Tahoe with the police package. 16.4" front rotors. However most engines retain stock internals with perhaps a little tuning help from the ECU.
Even with all of that the most you can do is your best to follow that crazy idiot who refuses to stop for some reason. You have to react to their moves and also what everyone else around you two are doing and that takes time. Time at high speeds equals extra distance. Even if you manage to stay right on their bumper how does one car get another to stop?
PIT maneuvers can be used but each department sets rules for when and where they can be used. Some departments don't mind killing everyone in the car because the driver refused to stop after making a right on red where you can't or some other low level traffic offense. Other departments have no pursuit policies unless there was a verified forcible felony just committed such as a kidnapping, rape, robbery, etc. The bad guys know who chases and who doesn't. Ultimately your command staff and a bunch of lawyers and judges will decide whether the juice you poured during the pursuit was worth the squeeze especially if someone is injured or killed.
So during a pursuit the things that run through an officer's head are: Will I get into trouble for this.. I could die.. they could die.. someone unrelated could die...I could be fired and lose my income...I could be sued and lose even more money.. I could go to jail...All while chasing someone in an uncontrolled environment with the possiblility of taking incoming gunfire when you are behind them, gunfire when you stop, a crash where you are incapacitated and cannot continue...