Depends what arrowhead you are using.
Barbed arrows easily sliced into flesh however when you pull them out you end up tearing large chunks of flesh with it, the only way to remove a barbed was to cut round it or push it through. Barbed arrows were also used to target horses, as once embedded the horse's movement would cause the arrows to tear the flesh and cause internal bleeding.
Bodkin arrows made of steel were what were used to cause major damage, they were able to pierce plate (not Milanese or other expensive plate, (but they could still pierce in some cases)) and the force of the arrow hitting you could send you tumbling backwards (even if it didn't pierce your flesh), or knock you to the floor. Then if you get knocked down you are either gonna get trampled by your own troops or the hooves of your allied cavalry. Either way, you are fucked.
As to bow types, it depends on where you lived. Eastern style bows were typically designed to be shot from horseback and to target lightly armoured infantry/cavalry as plate armour wasn't widely used in the eastern areas, instead boiled leather, furs, chain maille was in abundance. Whereas in Medieval Europe, plate was seen more as stature. - expensive plate shows off wealth - so longbows and crossbows were used to penetrate this mail.
^Just a quick overview