Nothing drags a chase scene (or ANY quick action scene) down like too much flowery description. The people involved in a chase scene are focused: one on getting away (or leading if it's some kind of trick), and the other on catching up. The one running will be trying to increase distance and break line of sight...if they aren't fast enough to do it quickly, they'll probably try to be clever and create obstacles, which may stop the pursuer dead or do nothing but slow down the one trying to get away. If they know the area really well, they can pull all sorts of environment-dependent tricks to lose the pursuer, from ducking into buildings to going around a corner, throwing off a jacket, and calmly walking back the way they came, mixed in with a crowd of pedestrians.
The pursuer is highly focused on the one running away and will be constantly trying to narrow the gap and, if they're smart, trying to figure out where the one they're chasing is trying to go. Even if you lose someone in a chase, if you know where they'll go afterward, you can just go straight there...sometimes useful, sometimes not. If the pursuer DOESN'T know where the one being chased is going, then it is vital that they don't lose line of sight for more than an instant, which means the environment they're both moving through is extremely important. Crowds, buildings, vehicles, everything is suddenly an obstacle. The pursuer will be trying to watch the one they're chasing, other people, vehicles, traffic lights, animals, and everything else to find the best way through to close a little more distance.
Chances are the pursuer will be hyper-focused and aware, but that can create tunnel vision as well if they're not careful, where they are only focused on the one they're chasing and run straight into a cyclist, or get hit by a car, for instance.