Sometimes if your speed is almost even, it will take forever to chase them down unless they're also looking for a fight - and waste valuable time, or let them regroup with others to bolster their numbers before turning to face you.
Stock up on extra horses when possible - it'll increase your movement speed on the map if all of your units can ride between battles.Trying to do everything on your own will get very hard otherwise. Be sure to take on the main quest to speak to 10 nobles (aka the leaders of each faction), even after the tutorial has ended, as it will speed up your renown and notoriety by getting to know each of the factions, and you’ll be able to pick a faction to fight for all the quicker.