On a battlefield the majority of a medieval army are peasantry living under the rule of their lords or Kings.
They're not equipped with heavy metal armour. This isn't a regimented highly-trained uniformed military force.
There are some with a few bits of metal plating, but most people are in loose clothes or padded in woolen items.
Against such an enemy I would prefer the Mace for it's blunt crushing power, breaking through any metal helmets worn and destroying skulls and necks. It also shatters bones inside the body and snaps ribs, stabbing them into internal organs.
The Morning Star is good at this too, but it's spiked. And spikes get stuck, as everyone knows.
Spikes will also get stuck easily when used against an opponent defending himself with a wooden shield.
The last thing you want in a confined battlefield melee is to get your weapon stuck in the body or shield of someone else.
At least a mace can crush through a shield or opponent. It can also be easily used to destroy the opponent's constructions, such as wooden doors and siege weaponry, like ladders.
The bonus to a Morning Star is against armoured knights, where it's piercing power can get into chinks in armour and occasionally puncture plate-metal.
That's a bonus over a Mace, because if you wound someone in a suit of armour, they will bleed out in it.
It usually takes two to three people to dress someone in armour and to remove it.
If someone is bleeding profusely within their armour, then there's no chance that it can be removed quickly and the wound tended to.
Against an enemy without such armour, it is possible to tend to such wounds.
But even here the weighted power of a Mace comes to hand, when it can crush armour and the occupant within.
Furthermore a smash to an opponents head wearing a metal full-helm may knock them out, or provide such a concusion or intense tinnitus that they are left highly disoreinted and incapable of fighting, making an easy kill.