I feel the main reason the treasure-trashing attacks (Thief, Pirate Ship, Noble Brigand) have tended to be a bit on the weaker side is because usually the strongest counter to these attacks is to just not play Big Money. All three of these do little damage to engines (and in the case of Thief and Pirate Ship, actually help the engine builder by trashing their Coppers), so if an engine is available, the correct move is often to skip the treasure-trasher and go for the engine. Pirate Ship is slightly different in that it can still be useful in generating coin for the attacker in the late game, but against action-heavy, treasure-light (or treasure-less) engines, Noble Brigand and Thief can actually be useless to the attacker since they will rarely, if ever, gain treasures in the mid and late game.
Bandit on the other hand is very different from these other three in that the "counter" of going engine doesn't hurt the attacker as badly since it always gains them Golds, regardless of what cards are revealed in the attack. Whereas the strength of other three is largely dependent upon your opponent's strategy (e.g. strong against Big Money, very weak against engines), Bandit doesn't need to flip treasures in order to "work"; instead, the gold gaining becomes the primary function of the card and the treasure trashing becomes an added bonus when it hits. With this in mind, I think Bandit-BM will definitely be vastly stronger than Thief-BM, Pirate Ship-BM, or Noble Brigand-BM against engine-players, but it's hard to say by how much.
I'll add that I do really like that Bandit is also its own counter, much more directly and elegantly than the other three treasure-trashing attacks.