there are subtle distinctions between what a pollaxe and a halberd are. but basically since both of them are multiple stiking surface polearms the clearest distinction to be made is that a pollaxe has a shorter haft and is generally more sturdily built. Both weapons generally will have a point combined with a striking surface and generally a raven's bill shaped hook. A pollaxe sometimes will have also a reverse side point as well as the spear point and sometimes will replace the axe blade or hook with a warhammer.
Because the pollaxe is shorter it generally is a bit more handy for closer combat as the shorter haft will not be as liable to hang up on friends and enemies and indeed can also be used as a grappling assist. This short handiness also contributes to the pollaxes fight time it can respond to or generate a new threat easily as fast as a hand and a half or single handed weapon, and due to it's range advantage can threaten either of these from well outside their ranges while still being dangerous while standing on one's opponent's toes. Either one can generate a tremendous amount of force, arguably more than a two handed sword, due to the weapon physics, this is the relationship between the centers of mass, balance and harmonic flexibility. In other words how close is the "sweet spot" to the center of mass.
The pollaxe is something I know a bit about as I have been fighting with one for about the past 10 years the top of the weapon too is remarkably good as a blocker as you can entangle and disentangle an opponents seemingly at will with a tremendous amount of leverage on your side.
What should this mean in game terms?
Well a pollaxe should act on initiative, it should have increased strength enough basically to ignore all but the very best armour. As it's blows are percussive in nature as well as chopping or puncturing armour ought not really to be a defence against this, or a halberd, since percussion can break a bone with the shock wave through armour as well as cause contre coup concussions severe enough to kill, again without puncturing or severely deforming a helmet.
We did some force meter readings with a real one, against a helmet and against an arm weighted target inside padding and steel.
but what exactly IS the armour save in warhammer, or toughness or a ward save.
I think I'm happy enough with this having a +1 to strength and AP of +1 or +2 attacking on initiative.
In my opinion though, no man made weapons would be made in such a way that a warrior would have to sacrifice his initiative. Those that did, would not survive the first battlefield encounter and be filed as a failed experiment, just ask those dead guys over there for confirmation. I mean really, a warhammer model pays nearly the cost of a base human (3 points) for +2S, the penalty of automatically going last I think is too high generally. I might be haggled into an initiative penalty -1 to ini but even that seems unrealistic and more importantly irrational to me.
This is speaking a bit to the concept of fight initiative, in my opinion initiative is something which should be fought for and which you can win. Racial initiative how quick you are generally, movement initiative what have you done to gain initiative before going into a combat, then Fight initiative what hacve you succesfully done in a combat to maintain initiative or done badly to lose it. Charging should be +2 ini, charging a flank another +1 a rear +2, cause fear +1, cause terror +2, stupid -2, cold blooded -1 and so on. In the fight itself wound counts balance each other out +- ini to the winner/loser, won combat last round+2 ini, fear and terror still count in combat as would flanks and rear, and outnumbering+1 for simple outnumbering +2 for doubling your opponent's #'s. It's a slightly different take on combat resolution, which can be calculated simultaneously to standard break test combat rez or incorporated into it. I think that this is more rational as it is possible that well played goblins can get the jump on overcocky elves, besides that this relies on well thought out strategy on the parts of the players as opposed to just dumb luck of the dice.
Terror causing, stupid coldone riders would for example have no effect on initiative but they might still make you think twice about fighting them in the first place.