Warning: There are always exceptions to everything I say, keep this in mind
I think the key thing is that you don't want to meddle with Provinces if at all possible.
This means that your build-up is going to be a bit different. You don't ever need to reach $6 for Gold and you don't even need Gold at all. With a normal Province game you need Golds, because a good ($8+) and a bad ($2-) turn is better for you than two mediocre ($3-$7) turns. So a higher concentration of money is good for Province games. You know, when you have those hands where you have $9 because your Golds are clumped together.
If you're going for Duke it's much better to have your money spread out. 3 Silvers > 2 Golds even though they have the same purchasing power. With money being more spread out, you'll reach $5 more consistently and this consistency is very important. A deck heavily flooded with Silver will likely hit more $5's than a deck with only Golds and Coppers which will hit the occasional good and bad turns.
Because you need to buy a lot of cards to be able to beat a Province player with 8 of them, you want the game to go long. How do you let the game go long? First of all, don't buy any Provinces, this will only help the Province player. Buying 4 Provinces is pretty easy, but going from 7 to grabbing the last one may take forever.
Second, you need to make sure the kingdom is right for it. Some kingdoms will let the Province player play a megaturn with Horn of Plenty or Bridge or something like that. But there are other things to pay attention to: Can your opponent trash the Provinces for benefit and thus rush towards the end without ending up with 8 Provinces in his deck? Salvager, Governor, Remodel and even Apprentice come to mind here, also Bishop and its special form the Golden Deck.
Something that can be advantegeous to the Duke player is the presence of attacks. Any decent attack can slow the game down to a crawl. Cursers, but also a sneaky Cutpurse can be very nasty. And Fortune Teller is looking good for a player with 7 Provinces in his deck. In those games it can be very hard to even get to $8 once. So if you make sure your deck is better suited for Duchy/Duke from the outset you have a better chance in those games.
