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While the halberd's blade offers a lot of options for hooking your opponent, it equally gives them an opportunity to hook your polearm and manipulate it themselves. The simpler spearhead is also lighter than that of a halberd, allowing for more sustain when fighting for long periods.

I would definitely prefer a halberd (or billhook) over a spear given the choice, but it's not as much of a direct upgrade as you might think.