Where Dark Ages forces you to consider the ramifications of replacing Estates with Shelters, Hinterlands has gently invited you to replace Silver with Oasis. Perhaps no other card yet printed fits Silver's "neutral <$3 supporting card" niche this well. As a result, this article is almost as much about Silver as it is Oasis; I'll examine the strengths and weaknesses of each. (With this said, of course it's possible to pass up both cards and buy nothing; or to buy one card early and the other later.)
First, and perhaps most obvious, is the money. Oasis gives you a card to replace itself, then effectively replaces your weakest card with a Copper. In the early game this is on average slightly inferior to Silver's flat $2, but a lot better than a flat $1 or $0. (A more nuanced look at the opening probabilities may yield further insight, and I might run some stats in the next draft if the community deems it worth making one; unfortunately I can't at the moment.)
Later in the game, the monetary values of Silver and Oasis can diverge more widely. A deck that trashes Estates might quickly find its Oases neutral or even detrimental, as it no longer has any targets which would benefit from "turning into Copper." Even without trashing, straightforward deckbuilding can often reduce the chances of Oasis finding junk to discard in a given hand. Notably, Oasis itself can interfere with another Oasis (although no more than Silver would interfere with an Oasis). For these reasons, Oasis is generally a poor fit in Big Money variants.
None of this is an absolute dealbreaker; Silver too can outlive its usefulness! But if you do opt to raise your deck's strength without lowering the proportion of viable Oasis targets it contains, you might find Oasis outperforming Silver somewhat. This could happen as a result of Copper trashing or some degree of Cursing (especially Sea Hags) from your opponent; or of buying alt-VP cards. Tunnel obviously fits here too. Another option is large hand sizes, which of course make you more likely to find junk even when there's less of it in the deck. By contrast, handsize reducers such as Militia or opponents' Bishops are very bad for Oasis.
The second point of comparison between Oasis and Silver is that Silver clogs your deck more. Silver slows down your cycling, and interferes with combos in a way that Oasis does not. All strong players have realized there are times when Silver interferes more than it helps (and yet, tragically, might still be unavoidable). Oasis is preferable in many of these situations, although it's still possible on occasion to pass over both Oasis and Silver and buy nothing. But even in games when Silver is perfectly tolerable, Oasis might be better. Oasis/Moneylender provides nice cycling for the Moneylender and enough money to transition into many different decks. Players who open Horse Traders aiming for $5 turns, or Potion aiming for Apothecary/University, may feel that their economy is really pretty sufficient; they just want to play the opener (and their $5 or $2P cards) more often.
Finally, there are the little differences, which mostly stem from Oasis's being an Action rather than a Treasure. Vineyard, Scrying Pool, and Conspirator enjoy it, while Bank does not. Against Pirate Ship it's a no-brainer. Any engine or card that can replace the card Oasis discarded will get a big boost, including Minion and the "Draw to X" family (and Scrying Pool, from some perspectives).
