As a longbowman I can say I do damage and that I am fairly deadly at medium range (long range like I thought I would be, not so much, despite having 160 archery wpf I'm still not accurate enough to hit my target 80% of the time, it's kind of a lottery).
I do believe that the longbow is balanced very well, because as an archer, I get one shot by someone with a warbow, 6pd and bodkin arrows from a hit to the chest, and i'm completely fine by that, the weapon is for dealing with light armoured targets, much like being smacked by a 2hander/polearm, I tend not to survive very well.
As a medium armour (9.5 lamellar armour and up) to heavy armour user you should expect the longbow to hurt.
Finally, I would like to point out the hit on that "armour plate" that that guy did, he hit with the longbow at the bottom, and the other bow in the middle, just work out why I would say that it wasn't a fair test... (His wpf wasn't high enough for the longbow as well)