I think there is a documentary on Qing weaponry. It mentioned that, due to their technique in creating their bronze sword, they were able to make it longer thus deadlier against foes that we using swords.
For the Dao, from Ming and onward, (again somewhere I read this) due to the the influence from Mongol weapons, the curve from Mongol swords influenced on the manufacturing of Chinese sword and this increased slashing effectiveness. If you take a look at the Dao, they also have a pointed tip at the end which can be used for stabbing. Also from what I read previously, learning effectively on how to used a Dao was easier than using Jian.
Like previous poster have said. There are different style of fighting, one for warfare and one for non-warfare (eg, assassination, self defense and others methods used for non-warfare) In war, soldiers are facing hordes of enemies with pole-arms. Cavalry will use Jian, Dao and bow for hit and runs. You will most likely be facing pole arms and and arrows in warfare, so Jian and Dao will most likely be used less. In "civilian life" Jian and Dao are most likely used than pole arms, since you have more room to maneuver and deflect pole arms more easily. In assassination, (I don't even have to explain this) you are not going to be using pole arms, but you will not be just using Jian and Dao. Assassins in China also uses specialty weapons or weird looking weapon to kill
In regarding to western armor, I always thought that it was the crossbow that rendered armor ineffective before gun power came into play.