I have been told that a moderately skilled pole-arm user is usually on equal footing with an expert swordsman
Who told you that? It's true that polearms are grossly under-represented in most European martial art groups/clubs today, so sword-oriented students are less likely to have experience in facing a polearm user while the polearm blokes, on the contrary, will be more experienced in facing swords. This creates a sampling bias in favour of the polearm--much in the same way that the numerical prevalence of right-handed fencers gives left-handed ones an advantage in modern sport fencing. Back in the medieval and Renaissance times, many students (especially those from the knightly and noble social classes) would probably have had to learn the use of
both swords and polearms, which is likely to have given them a better idea of how to face polearms with the sword.
This raises the question of how can a swordsman defeat someone with a spear or pollaxe?
What are your thoughts?
As
the polearms guy in the local club back when it was still active, I can tell you that I always felt a certain measure of anxiety about my hands since the spear, the pike, and the poleaxe don't have the prominent cross of a contemporary sword, which means that many manoeuvres that would be commonplace with the sword may put the hands at considerable danger when performed with a polearm instead. A perceptive swordsman ought to be able to exploit this anxiety over the hands by employing feints to threaten the hands before moving in to strike a more important target.
(On the other hand, a polearm user expecting earnest combat against swordsmen should really invest in some hand protection. In historical terms a gauntlet would have been a very,
very good idea).
What swords would be most effective?
What techniques or tactics would be most effective?
Any sword will work if the swordsman knows how to exploit the specific advantage of the sword vis-a-vis the polearm. For example, a two-handed sword is something of a polearm in its own right, allowing the swordsman to engage a polearm-toting adversary on a more equal basis. On the other hand, a single-sword user would likely try closing into grappling distance since the shaft of a polearm is more amenable to a grab than, say, a sword blade (although by the same token a polearm user could lure a single-sword man into a grappling attempt prior to bashing him with the butt or the shaft--or using the grabbing hand to set up a lock or throw if the swordsman refuses to let go).
How would armor come into play? Would certain weapons or techniques be especially effective or ineffective in armored combat vs. unarmored comat?
This topic is too broad and complicated to be addressed in a single post (especially considering the various levels of protection available to medieval and Renaissance combatants), but in general you'd want armour on both sides of the equation--especially hand protection for polearms (I've explained why already) and leg protection for swords (because a longer polearm with a reach advantage is likely to go for the legs from beyond the range of a Scheitelhau or similar technique with the sword), not to mention head protection for both (I don't think I even need to explain the reason for
this).
I am assuming that the tactics and techniques would all be about what way works best to safely close the distance.
Not really. With shorter polearms (such as the poleaxe or Paulus Hector Mair's short staff) the butt is as deadly as the point or axe/hammerhead. Getting past the point is important but the swordsman still has to be prepared to fight at all the ranges (Zufechten, Krieg, and Ringen / large, close, and grappling measure).
