The way I handle personal-scale chases is a competitive check. Whoever wins the check moves one movement farther away/closer. If one person succeeds and the other person fails, the winner moves two movements farther away/closer.
Personal-scale chases generally end in a “We got you!” or a “We lost them.” not so much a distance matter.
Each round of the chase is one check: I propose two different skills (and their difficulties) that could be used, and the skill/difficulty used by the opposition if they choose one or the other.
Each PC rolls their check, and we compare it to the results of the opponent as per usual.
Examples: Average Coordination to weave through the crowd, upgraded once since you’re being pursued by cops, with 1 Setback because of the density of the crowd. The cops will make Average Coercion to get the people to move out of their way.
Or, Average Cool to run through traffic, upgraded twice because of the risk of getting hit. The cops will have to make the same check to follow.
The simplest is always Athletics vs. Athletics, but that’s boring.
For Stealth, I make the check a competitive Stealth vs. Perception check. If you succeed and they fail, they lose you (but you aren’t out of it yet!). If you win the check, but they succeed, they lose track of you long enough for you to gain on them, but they catch sight of you again and keep following.
In this case, the difficulties will likely be inverted. So if it’s an Average check for Stealth, it’s Average for them. If it’s Easy for you, it’s Hard for them, and vice versa.
(Perception instead of Vigilance because they are actively watching you)
I’ve only tested this a couple times, but it worked quite well and was well-received both times.