I'm a very defensive general, fielding lots of archers and a siege engine or two.

I think this behaviour has been hammered in through the last few titles, where firing at an advancing enemy was often extremely effective, especially in RTW/M2TW with their rather extreme battlefields (mountain sides).

I find that defending a hill is sometimes actually not as effective anymore, because the enemy can fire back as soon as your archers can fire at them, and the AI always sends his archers out first, starts firing, and then send in the infantry. My Ashigaru line gets decimated by the enemy archers if I place them in front of my archers, and if I place archers in front, I lose time when I have to pull them back. I think the most viable tactic is to counter charge downhill when the infantry approaches my archers, but this works best with katanas, and using that makes me vulnerable to center cavalry charges. I mix these approaches up a bit. I often use a mangonel or two, since it often makes the AI attack my position even though I'm technically the attacker, and they can be really devastating if you know where to aim as the enemy advances. They take out a whole lot of horses when they hit cavalry, and can of course be used to cheaply eliminate the enemy leadership.

I rarely rush per se, the battles where I am forced to go on the offense are very slow at first, I skirmish intensly to get the upper hand in an archer duel, or attack a flank with archers, and then I might rush if the AI re-arranges to go for my exposed flanking archers. I almost only use cavalry to charge archers left alone behind the clashing lines, I find that reduces casualties more than charging the rear for morale shock, since arrows are so lethal.