The system of armor could be better, but I have severe reservations about a rock/paper/scissors style of armor.
I wouldn't want to see a system such as "pierce beats plate, blunt beats chain, cut beats cloth" because, for the most part, it makes no sense.
For instance: everything beats cloth, not just cutting weapons. If you're wearing cloth, you may as well paint "shoot me" on your chest and jump up and down spastically to draw the attention of the enemy archers.
And while chain may not be as good at blocking blunt weapons as it is at blocking edged ones, you're still a hell of a lot better off wearing chainmail than wearing cloth (or nothing) when you get whacked in the sternum with a hammer.
What I would rather see is an exaggerated version of what we already have in place.
So in short:
Platemail gives better protection against all damage types than all other kinds of armor. However, it protects you less from piercing attacks than it does from other kinds of weapons. As for cutting weapons, however, it's almost impossible to hurt a man in plate unless you're wielding a very monstrous weapon. However, it also encumbers you more than all other armor, reducing your movement and attack speeds.
Chainmail gives, on average, the second best protection. It protects you less from blunt damage than from other types of damage, however, and encumbers you.
Leather armor gives fairly low protection. It offers a little protection against blunt, piercing, and cutting attacks. It does not inhibit your movement much.
Cloth (or no armor) offers almost no protection against all types of weapons. In fact, those wearing cloth perhaps should take extra damage from piercing and cutting weapons due to the internal damage they may (and probably will) suffer at the hands of enemies. On the bright side, there is no encumberance to worry about.
Just my $.02