At first, it looks like a Woodcutter variant, but is probably a bit more like Bridge in the sense that its power grows as you buy more cards. Really, Bridge can be seen as a Woodcutter variant itself. In fact, if you just buy one card through Bridge, it's essentially a $4 Woodcutter. Each buy you make with Bridge, though, would be nearly the same as increasing the amount of money given by Woodcutter by $1. The same goes for Highway, i.e. Treasury without the replacement bonus in non +Buy or Virtual +Buy games. There is the whole wonkiness when cards drop to $0, but you get my point.
Anyway, let's look at some situations to compare Bridge and Cardname (I'll call it "Jeweler," because I can). If you wanted to buy, say, a Caravan and a Silver with Bridge, you would need $4 in other funds plus the $1 from Bridge. Since the costs of Caravan and Silver both drop by one, you can buy them as a $3 and a $2. Had you played Woodcutter instead of Bridge, you'd only have $6 among the two buys, which is not enough for the $7 total. With Jeweler, you'll have $6 to start with. However, if you buy the $4 Caravan, you get the extra $1 to get you the $3 Silver. It works the other way, too.
Now, let's say you have $3 in other funds, but you want to get a Gold. With Bridge, the $1 bonus and the $1 discount only give you $4 for a $5 Gold. No dice. With Jeweler, you will have $5 for a $6 Gold. However, if you buy a $0 card (Copper), you'll get the $1 bonus that will give you enough for a Gold. Of course, now you have an extra Copper to meddle with. If you don't have trashers, Trader, or cards that benefit from Copper, you have to wonder whether it's worth it.
Finally, let's say there are two Provinces left, and you can win by buying both. You have $7 in other funds, and you have a King's Court and either Bridge or Jeweler in hand. If you KC Bridge, you now have $10 to spend on $5 Provinces. You can buy both and win. If you KC Jeweler, though, you'll have $13 to spend on $8 Provinces. Since this has the "in play" caveat, you only get $1 bonus, leaving you with $6 after your first Province buy. You can be smart about it, though, since you have four buys now -- buy two Coppers, which will give you $15 and two buys left. Buy a Province, which will take you to $8, then buy the second. It's a little less intuitive, but just as effective.
What about the KC-KC-Bridge-Bridge-Bridge alternative? Clearly, you can clean out the Provinces (in a 2p game, anyway) by doing this. How about with Jeweler? You have $18 and 10 Buys. Since the last doesn't count, you would have a potential extra bonus of $27, leading to a potential total of $45. To clean out the Provinces, you'd need a total of $64. Not happening. You could only get a maximum of 5 Provinces without extra help. While that's still good, it's not a cleanup in aisle three. In this case, Bridge is clearly superior.
Now, what if Bridge had the "in play" caveat in both instances? The KC-Bridge example would still have $10 to spend, but the Provinces would be $7 each. You could only get one. KC-KC-Bridge-Bridge-Bridge would only reduce the Provinces to $5, and with $9 to spend, you'd only get one. Jeweler, conversely, gets you 2 and 3 Provinces, respectively, given that you load up on Coppers. Alternatively, if Jeweler was worded like Bridge, you could use the double KC trick to clean out the Provinces, since each Province buy actually nets you $1. In fact, you could clean out the Colonies with KC x2-Jeweler x3 -- You'd only have a net loss of $2 per buy, and since you start with $18, you could get 9 Colonies total (compare to $9 for $2 Colonies through the Bridge method).
Therefore, if "Jeweler" and Bridge were worded similarly (i.e. both could stack through TR/KC or both couldn't), Jeweler would be a far superior card. As it is, there are times when Jeweler is superior and times when Bridge is superior.
Hooray, I caught the major Bridge comparison. Of course, I completely missed the Workshop/Ironworks and Salvager/Apprentice interactions, but otherwise, yay.
ETA: Fixed the goof in the KC-KC-"Jeweler" x3 paragraph. Thanks, Razzishi.