| Dr z0b |
The real problem is that there is no rules to take into account the difference between the handling of different weapons. An axe should do much greater damage than a sword, but a sword is a more responsive and accurate weapon; better at hitting small targets and finding a chink in armour, much better at parrying. Whilst an axe doesn't need to find a chink in armour; it just crushes its way though.
A falchion would be somewhere between the two, and a rapier would be even more responsive than a normal sword.
Shields should also add a lot more to AC but are generally made of wood and would probably start to break after a few rounds of heavy combat. There is no way you would block a two handed axe blow with a shield, it would cut straight through the shield and into your arm.