Let's quote Ferne.
GE: In the battle with Greg… er Gilgamesh, he attempts to attack you with what some players might assume to be the Bradamante only to claim that it’s not the powerful weapon he thought it was. Where is the real Bradamante? Is there any connection to Turn 4 of the Second Binding Coil?


MCKF: Back in the day, Nael used Bradamante. We know that that is a fact. Back in 1.x you have your battle with Nael van Darnus and you defeat him. As the area crumbles around him, Bradamante falls.

Then, a Coerthan merchant finds the Bradamante, and who does he sell it too? Some old guy that that uses it as a gardening tool in Thanalan. He decides he can’t use it and just throws it in his field.

Then…guess who finds it? Hildibrand! He tries to use it and has his ass blown off and it just falls away into Thanalan.

Who finds it after that? Gilgamesh! He picks it up and from there you know the rest. So yes, it is Bradamante, the one that Nael used.
He retraced the history of the weapon, and specified the weapon Gilgamesh uses against us is the one Nael wielded. There's no real reason to find another explanation when we were directly said it's the real one.

As for why Gilgamesh says "I've been had!", it might simply be that someone told him it was the strongest of spears, and only realizes it's just another gunhalberd.
Now, "Pradamante" is weird, but it might simply means it's far from as powerful as he thought it was

It's not like it's an ancient weapon, reforged with rare salts, tremped in hydra's blood, infused with mystical mist, souls of countless monsters, and who proved itself after some long trials, before being infused with the purest form of materia you could find... GTFO FROM MY WEAPON GREG, IT'S MINE