If anything, cops are almost too easy to get away from in this game! There are tons of places that cop cars and helicopters will never see you.
But I think that all depends on the person and car, especially if you're in a vehicle that you can't ditch.
In SP I tend to drive high-end cars but that damage really easily. A minor collision and one of the front tires will jam inside the wheel well and now you can't turn for sh*t.
Online though I unintentionally ended up with the Weeny Issi (Mini Cooper) as my personal car and that baby can recover from collisions in seconds, turn almost on a dime, and fit through tight alleys like you wouldn't believe. She's not the fastest thing on the road but I can out maneuver the cops every time in that car like I never could in the high-end cars.
I was even being chased by another player trying to kill me. He had a much faster muscle car that was gaining on me, so I just made a bunch of turns. He spun out every time he tried to make the same turns and could never catch me. And my car has only the basic free upgrades I got in the beginning!
Goes to show skill beats brute force.
One thing to note: From my experience, you can't jam your wheels and have them locked up like you can in single player.