The Cop Car is a four-door sedan, compared to the Stiletto which is a two-door coupe
This is the suspected "Destiny" seen in one of the trailers. It's a four-door sedan which has the same square headlights, side indicators, grill and hood ornament as the cop car above.
One of the recent gameplay demos showed SWAT troopers.
So far we have identified three police vehicles; a modern patrol car, a 1980s-style patrol car and a SUV; the latter of which comes in both Police and SAWT versions. We've seen both the Opressor and Tornado, vehicles that have been used by...
Some of my own finds
Unknown (Saints Criminal Customs DLC pack)
Fury (Los Panteros American Muscle Bundle)
Big Willy's Taxi Company
Unknown (may be civilian version of Police/SWAT van)
Unknown (Possibly Criminal?)