The problem is the rules, in most Re-enactor groups you aren't allowed to grab the haft of an opponents polearm which is probably the number one technique you use against a spear, staff or polearm as soon as you get into any kind of bind. In many re-enactor groups you aren't even allowed to attack their hands. The rules also can effect the polearm user quite a bit too because they often aren't allowed to strike with the spear 'butt' or trip or use a variety of other fundamental historical techniques which appear in the European fencing manuals and exist in the martial arts traditions in Asia.
I agree with that. People always want simple answers to these sorts of questions but it's never that simple.Generally, the more armor swordman has, the easier he can handle the reach and polearm ability to counter his closing in with short stab or whatever.
But again, the more armor involved, the less useful most swords become.
So in all, as always in such broad matters, nothing can be called simply better than something else.
It's a mistake to say swords dominated the battlefields because spears and bows etc. were the primary weapons.
On the other hand it's a mistake to say that swords were not critical on the battlefield because the sidearm was so important. Armies equipped with swords and spears had a significant advantage over armies equipped with just spears or spears and knives or spears and axes.
That is why they went through the (comparatively) huge expense to make them, and put up with carrying them and maintaning them. Not fashion :)
G.