I'll only speak for one aspect of the Vandals in that, while certainly proving to be just as if not more destructive than the Huns and Alaric's visigoths--in terms of the sack of Rome they actually proved to be far less Vandal-like.

Like when Attilla and the Huns were at Rome's doorstep, Pope Leo I once again rode out to meet the would-be invaders and attempt to turn them away from the city. However, Leo's position with the Vandals was far weaker. They were far closer to Rome than Attila was, and Leo didn't have the benefit this time of an army at his back. Unlike the Huns though, the Vandals were christian.

What this is leading to is that when the Vandals did sack Rome, they made an agreement with Leo. They would take what they want--but they wouldn't harm the citizens. They stuck to their word. The Visigoths certainly didn't do that much.

Though, the Visigoths had a far better reason than the Vandals for wishing to sack Rome in the first place. Alaric wanted to establish a homeland for his people--and attempted multiple times to seek some sort of settlement Honorius. Honorius was too stupid or stubborn to accept Alaric's peace offers.

Things are not very black and white in history. While I can't speak of to how the act of vandalism became overtly associated with the Vandals, I can at least say that their sacking of Rome proved to be far less brutal than the other barbarian invasions of the Western Empire.