Quite a few war hammer designs have both a pick side and a hammer side. I was just wondering why these two? They're both geared towards defeating armour but in what situations would you use one over the other? Would it not make more sense to have an axe side and a pick/hammer side since the axe would be more effective at tackling light/no armour while the pick/hammer side would be better suited for armour?
This isn't history, more reenactment fighting or physics. Here's a viewpoint, you can try it yourself at any HEMA group
Axes and Picks twist away if they hit plate Armour on an angle, transferring little energy. While (Round headed) Mauls/Maces and (flat headed) hammers bounce, hitting the flesh inside with the energy transferred to the mail or plate. This becomes important if you're hammering on neck, knees, and other joints, where you can take enemies out of the fight without wasting making holes in their armour first.
If a pick comes in near perpendicular, then the small tip and medium weight, gives a high PSI that can penetrate the plate (and risk getting stuck). And an axe with a wide tip and the same weight will have a lower PSI so reduced penetration. Axes popularity comes from being useful between wars so mass produced and common in the peacetime. Picks have less civilian uses.
But uniquely Picks and Axes can "hook" people. Pulling armored people off their horse or their legs out for under them, or their weapon from their grasp. They can then be neutralized by standing on them, where your weight, your armors weight and their armours weight combine to pin the prone person in their Armour. Stamping your weight on a prone opponents joints can wreck the joints. And shoving long thin daggers in their gaps in their Armour while they're immobilized can blind them, deafen them, neuter them or make them bleed out.,
Armour is weight. It will help against weapon impacts fighting at arms length, but handicap against grappling.
Modern day HEMA (Historical European martial arts) injuries when fighting with blunt swords show
""In terms of injury rate (IR), 60 participants (22,3%) obtained head injuries. 36,5% sprains, 28,3% strains, 10,4% fractures and 5,6% dislocations. 40,6% subungual hematomas (swordsman’s thumbs/fingers) demonstrating you don't need to hole armour to wreck the wearer