I actually use a racing skill, which covers all situations where you have to chase someone on foot. Let's face it, I don't need a skill roll when there's no chase, so the skill is only used when you actually either want to escape someone or to catch someone. It covers actual sprinting, but also manoeuvering in a cluttered environment when chasing someone, and performing parkour-like acrobatics stunts in those situations.
I don't use actual movement speeds. If one of the protagonists is noticeably faster than the other, they might get a bonus to the roll depending on the environment, but in most cases, how you use the environment is a greater factor than how fast you are. The skill covers all of that.
The Riding skill is used in a similar way. People know how to ride a mount or they don't, there's no need for a skill value for that. However, their ability to catch someone else or to escape pursuers is what interests me. Riding also covers the ability to fight effectively on horseback (no roll needed, just use the lower of the Riding and the combat skill. If our mount is not combat-trained, or if the conditions are adverse, you need to spend one or more APs to control it, which reduces your ability to fight effectively).
