You should rename that to Most Useful Weapon, because Favorite is a matter of opinion and it seems you've already made up your mind about which weapons are the most useful. Besides, rarely is a weapon anymore useful than for it's combat potential in any installment.
Buster Sword may not have served a mechanical purpose in the game but served as a nexus connecting Cloud's past and present. If it wasn't important, it would have been a throw-away weapon like every single other item in the game. Barret's Gatling Gun-arm is the basis of his prostetic and while he can attach new parts to it, the Gatling Gun is apparently never removed thus it being an indispensable weapon as well.
In XII, the Sword of Kings and Treaty Blade are both used for cutting nethicite and are thus also key items.
If we were to realign the parameters to define most useful by realistic terms, all of the huge swords would be disqualified as no could realistically defend themselves or quickly dispatch enemies with such heavy equipment. Joke weapons (even if they are the most powerful in the game) would also be disqualified.