In regards to the argument for spears doing well against armour, I think the poster's above videos best demonstrates the usefulness of some, but not all spears. A simple leaf bladed spear for example does little against western medieval armour as it's likely to glance of, perhaps hook onto something but likely do little damage. Halberds, dagger-axes, pole-axes, the spear mentioned in the video above; these are all spears that handle armoured foes exceptionally well. But again a spear is limited in that in a clustered battle it becomes difficult to use.
Thus I think, personally, the war pick (the hammer and pick option) is the most effective in combat. Either end can brutalize armour, smashing in armour or piercing it completely and ringing the man inside. Not to mention against someone unarmoured it would do even more damage.