I find it dubious to give that advantage
If both players have the same movement speed, literally nothing happens when people chase other people. Especially in a world where the person being chased just picks up speed boosts which causes permament distance between the 2 parties. I dont understand why you even make inputs and suggestions on mechanics and power balance when you dont even know what you're talking about.
The game already has mounts and ships that can move faster than anyone on foot. I haven't had the chance to use them yet, but it seems like they should be the ultimate trump card in foot chases.
Horses are busted in PVP because you just run ahead of people, teleport ahead of people through thingwalls or roads and catch up to those who dont have horses or have ran out of pony power, making escape literally impossible. When it was possible to use horses it was a total fiesta for everyone involved and none liked it so now we dont have horses.
Big boats are used as escape tools and its working fine because both sides have usually have access to them which creates interesting dynamic situations where you still have to at some point disembark and you will continue getting chased on land.