Apart from both being deckbuilding games, Ascension and Dominion are a world of difference. I love both; I think Ascension is more fun with 2p while I prefer Dominion with >2p, although I have yet to try Ascensions 2v2 mode, which supposedly fixes a lot of the gripes I have with >2p Ascension.
The player interaction in Dominion is mainly through attacks, which you can see coming from before the game starts and you can (and should) plan for that. Interaction through the "marketplace" is very limited - the PPR and perhaps leaving a pile at 2 or 3 cards to prevent a 3-pile ending. Other than that, it's pretty much a racing game, find the most efficient route to collecting VP while simultaneously ending the game. Or in other words: design what you want to do, taking into account the possible actions of your opponent(s), then everybody builds his design and we will see who hits the finish line first. I find that if I have chosen the wrong strategy or just have really bad luck, I can only catch up if the opponent has made a (number of) mistake(s) as well. (I can't do anything my opponent couldn't have seen before the game has even started; and he could have done it himself)
The player interaction in Ascension is mainly through the marketplace, which is variable and unplannable; and consists mainly of allowing/denying cards to your opponent. Attacks are as unplannable as everything else and in addition also a bit weak. It plays out much more like a boxing or football match - you do something, the opponent responds, you respond to that response and so on. If I make a bad decision or have bad luck somewhere in the game, I can adapt to try to turn things around. The analog would be that we are both on the same train, we both have a speed control for the train, and stuff swings by as we go along and we each have to make the best of what is thrown at us.
As for the actual cardplay - I find both games have equally meaningful decisions in that area. It's not like you are often not going to buy anything with a $6 hand in Dominion either - it's just the decision between gold and $5 action that can be interesting. That sort of stuff is also in Ascension - buy what's obviously reasonable, buy something cheap just to rotate new stuff into the marketplace, or not buy something from the marketplace to prevent new goods rotating in for your opponent. Also, the always availables in Ascension are about as good or bad as silver is in Dominion - that stuff helps but can also really get in the way. I very often let 2 or 3 runes unspent when I see nothing good/affordable in the marketplace and I also don't feel like I would improve my deck with any of the always availables (and indeed, in Dominion you sometimes dump a $3 hand straight in the discard for the same reason). I also sometimes NOT play the banish-from-the-center-row cards when I don't see anything of value for my opponent.
In summary, if you think you will be getting Dominion, you will have a bad time playing. Then again, the same can be said about Carcassonne, Settlers and, well, anything that's not Dominion.
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As for the actual iOS app - it's awesome. It's as awesome as Isotropic is for Dominion, only prettier and with some (not so smart) AI. Only no in-game proper matchmaking. oh well.