Cut is the type of damage that gets lowered the most by armor.
Blunt and pierce are similar in terms of how much armor it ignores.
With an example with random numbers: if we say somebody has 60 armor, attackin him with 30 cutting damage will in fact only score maybe 15-20 (again I repeat, I'm putting random numbers) but with the same damage, a 30 damage blunt/pierce will do, let's say 28 damage. So against tough armored opponents, using blunt or piercing weapons is the way to go even if stat wise, the cutting weapon seems to do more damage.
So in résumé:
"Cut" is best against low armor
"Pierce" is the best at ignoring armor
"Blunt" ignores a little less armor than "pierce" but can sometimes knockdown/crushtrough (depending on the weapon, not all blunt weapons can crushtrough).
Edit: Look up this link like said previously:
http://infinitum.dyndns.org/crpg/calc.htmYou can calculate the damage difference by simply changing the damage type.