Interestingly, the most effective technique fro the sword user seemed to be to bull rush the spear user. This didn't work very often for the people in the video, but the rusher consistently got past the spear and had an open opportunity to finish of the spear user. it was just the sword user wasn't very good once the got past the spear. It also makes me think that wearing heavy armor would actually be a good thing, despite what @Son of the Serpent
suggests. Per that video plate would deflect about 90% of the "killing" blows in this video. That was something else I wasn't expecting.
Yes; sword user has to get in close; neither spear nor sword are good vs plate armour, but at least a sword can be half-sworded or murder-stroked with the guard. A dagger would be better, but you really want a specialist can-cracker like pollaxe.