Why would I choose anything other than a Greataxe as my Warlock Pact weapon?

In the PHB p.107 on Pact of the Blade boon it is stated:

You can choose the form that this melee weapon takes each time you create it (see chapter 5 for weapon options). You are proficient with it while you wield it.

Why would I ever choose a “low” damage weapon, compared to a Greataxe (for example) with its 1d12 damage? I’ll be proficient with whatever weapon I choose, anyway.