If you win the first major engagement and you are still relatively intact [attacking], I find sitting at the edge of the map routing the AI off can have its disadvantages.

It can be great for winning that battle in the short time, but in the long term it can be worse.

You really have to give the AI a bit of space so when you rout him again, you have a good chance of capturing/killing more routers, otherwise when rout him on the edge of the map most of his forces will still be intact.
If you are playing MTW 1.1 like me the AI always brings on cavalry and then rabble second anyway, so you ALWAYS have a big advantage over him (your balanced army vs his unbalanced one) and should win relatively easily.

When attacking, I tend to attack with my main balanced army and bring on light and fast reinforcements such as gallowglasses and cavalry who get to the battlefield fast and can act as impact shock troops. Cavalry is also more decisive later on in the game and much more effective when enemy forces are tired, so I find it better to bring the bulk of it on later rather than sooner.