Knights fighting with poleaxes at Portchester Castle
Portchester Castle in Hampshire hosted a 15th century "Wars of the Roses" event organised by The White Company during the mid 1990s. Similar equipment would have been used at the Battle of Bosworh in 1485.
Two fully armoured soldiers fight with poleaxes. By the 15th century heavier armour required heavier and longer shafted weapons to piece or buckle the plating and killed the opponent. If his legs could be cut from under him and he was knocked to the ground a swift dagger thrust through the visor slit would be enough, however much armour he was wearing.
The poleaxe was a gentleman's version of the infantry bill. The head was heavier and re-inforced and there was frequently a butt spike to make both ends an effective weapon.
Peasants often fought with 'Robin Hood' style quarter staffs. The poleaxe and the bill have been described to me as "quarterstaffs with attitude".