Simple - general killing.
Good artillery especially, but also archers, can take out a general that can in some cases pancake morale in the remaining army.
Defensively, especially at a bridge, they are devastating. In an open field battle archers are less effective but the concentrated firepower of three or more cannon can really take the wind out of massed enemy troops. When the first lines engage you can continue to pummel the enemy by firing over their heads.
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