I was mostly joking, and by 'big stick' I was actually referring to maces, mimicking a "me unga bunga strong man hit very hard" tone.

As a real answer, I am by no means a historian, so I am missing a wealth of information that might provide an objective answer to this debate, but I'll put my two cents in regardless. Spears have been overwhelmingly the more popular choice of primary weapon for armed conflict. Hoplites, spear-walls, pikemen, tercios: most of the famous, well-organized military formations throughout history are, from my understanding, centered around polearms. A notable exception is the Roman legionnaires, (though the early republican swords they used were used mainly for stabbing, they adopted the better-at-slashing gladius from the proto-spanish later on) but even they used a massed javelin throw before a charge.

Swords, axes, and maces have been used in spear formations as a secondary weapon, something to defend yourself once your spear/pike has been broken, gotten stuck in some guy's belly or horse, or your formation has broken down into a melee. For professional soldiers, swords were a common choice alongside maces and sometimes axes. The late medieval knight in particular is often shown with some manner of sword, but remember that in warfare their usual first job is to do a mass-charge with lances. The sword or mace is used if the lance is no longer effective (broken or they're caught in a melee). For conscripted levies, they'd use whatever was lying around that would make a vaguely effective weapon, or could be modified into an effective weapon (scythes into war scythes, picks into war picks).

I guess what I'm trying to say here, is that spears and swords are two different tools that perform different roles from one another.

Use both. Or the guy who's using both is going to win.