EDIT: modified as suggested.
Noble Brigand is one of the cards that I grow to like more and more in Hinterlands. I didn't quite realize he is using a bow though.
The initial buzz of the card is basically "Wow! Thief is officially admitted as an under-powered card!" This is quite a sound statement, as Noble Brigand is pretty much better in every way except one:
Thief trashes copper and helps your opponent. Noble Brigand does not; it even stuffs coppers to your opponent. Thief offers no immediate benefit to yourself; there is +1 coin from the Noble Brigand. Thief only works when you reshuffle and draw it, but Noble Brigand acts a full reshuffle earlier, right at when you buy it. The only potential downfall is that he cannot steal kingdom treasure and platinum.
With so many reinforcements, however, the Noble Brigand is still not a power card at $4. It is still a terminal action that does not draw any card. It provide less virtual money than Militia, and does not attack as reliably either. Therefore, it is not a card you will always consider to buy. To put it more directly, it is probably one of those cards that you will never make a fatal mistake by ignoring it.
That being said, in many situations, the Noble Brigand can bring a marginal benefit to your deck, usually just by the on-buy effect. In a BM-ish deck, a middle-to-late-game $4 turn can be better spent on a Noble Brigand than a silver or an estate, simply in the hope of flipping one of your opponent's important gold/silver. It isn't bad at all even to skip over his actions or cause a reshuffle at the wrong time for him. An early Noble brigand, however, when flipped the opponent's coppers, may prove to slow yourself down from that gold or $5 card a bit too much and accelerates your opponent at the same time. (Or according to WanderingWinder, Geronimoo, and the simulator, maybe not?)
There is a niche use of the card as a opener. When you are second player with $4 in hand in your first turn and when the first player have bought a silver, you will have 2/6 chance of getting that silver and trigger a reshuffle with the initial crappy cards at the same time. It is fun to use and see it works, but when it doesn't, you are facing quite an up-hill battle. The situation improves significantly with more players though, and it helps negate the disadvantage of the third or the fourth player quite a bit. They still have to have $4 in their first hand though.
Similar to Thief, the Noble Brigand can be quite important in a chapel game with no virtual money. But it proves to be a lot more dangerous in this case. To an unsuspecting opponent, getting one of his critical silver and gold can be fatal. And you don't need to buy it and use it, so he has no alert prior to the attack. Also the on-buy attack cannot be stopped. In addition, one can allow to buy multiple Noble Brigands to keep the pressure in such game, as extras can be chapeled away. This is one of the rare situations when I would say overlooking this card can be fatal.
That's probably it. There is no magic to make the card suddenly powerful. I like what Donald said about the card though: it is designed to be fun. It is indeed fun to attack when you are buying a card, especially when it does not force a degenerate game like IGG does. For myself, better yet, it is just powerful enough to try to win using it, and still underpowered enough that when I lose with it I won't be mad about my own luck.
Work with: Chapel, Gold, Silver, deck inspection attacks
Work against: powerful terminals, Venture, Platinum, Bank, cards that offer virtual coins