It's all relative to the unit itself. There shouldn't be clear cut stone-scissors-paper. Some of the decent 2 handers (like dismounted english knights) should be able to crush most infantry. While some should get torn up by decent swords.

I think most people view double handers as higher attack, lower defence. Something to smash through infantry quickly, yet lack the staying power of more armoured units. Though you also have to remember that a lot of the double handed units are so armoured they don't *need* a shield, so being a double hander doesn't necessarily have to mean a unit is vunerable. If I recall, towards the end of the medieval period knights stopped using shields because plate armour had become so effective it wasn't needed.