Another point to be considered when looking at possible types of weapon - on a medieval battlefield the main concern was taking your opponent out of action - it didn't matter whether or not you killed them, only that they couldn't kill you. So, a quick death in battle was often the exception rather than the rule (hence the 'misericorde'
http://en.wikipedia.org/wiki/Misericorde_(weapon) carried by warriors to dispatch wounded foes with a quick stab through the eye socket into the brain after the main fighting was over). A heavy weapon like an axe will do that more quickly & effectively than a sword (short or long), particularly if your opponent is wearing armour - an axe or hammer blow would break bones even beneath plate armour, let alone mail.