Poke horse so it doesn’t run into you

Hook rider to drag him off the horse, or at least control his movement

Axe rider when he’s vulnerable

Where the halberd is a very long weapon really only useful while fighting in formation(hooking and proning armored foes so your pikemen can finish them off), the Poleaxe is actually wieldable outside of formation and can do everything the halberd can do.

Have an opponent in maille? Stick 'em with the spear-point.

Have an opponent in plate? Hit them with the spike/hammer(there are variations on the poleaxe).

Have an opponent that can’t afford armor? Axe 'em, poke em, smack em, do whatever!

Plus! It’s a polarm weapon, which means you also get all the fighting benefits of wielding a staff!!