So for a chase scene throughout a city, I would think I would have the players and the person being chased an athletics check to see how fast they run, maybe some dex checks for avoiding obstacles. My questions arises when my monk who has a movement speed, higher than the the thief would just say, I immediately catch up to him. I know DM has the final say but what would you guys say? I just feel this just removes the idea of a chase occurring or being able to run away.
This sounds like a good old fashioned skill challenge :)
Sure, if the Thief and the Monk are racing across the Death Valley hard pan desert, the Monk is going to win.
But the thief can dodge, and climb, and run over rooftops, or grab a disguise, or spook some tied up horses into the street to block the chasing Party members, take shortcuts the Players don't know about, or ...
I agree. Lots of skill checks. The opponent who you’re chasing can make a deception check, for example, to slow the party down while the party can make a perception check to stay close. And all sorts of similar checks.