The manual calls them Runes and Power, so that's what I call them ;). And maybe the Cultist does need two Power to defeat, yeah, I may have misremembered that (hey, I've been playing Sentinels every weekend since around September, I can't fully remember every detail - blame GtG for that ;)). And no, we don't have any expansions. I'd never even considered that there were any, actually (until that thread where the tale of the bloke who used the game to propose to his girlfriend - I think an expansion of some kind got mentioned there).
Based on the description, I think I prefer Ascension to Dominion - I like the randomness of it, the way you don't know what cards are gonna come up in what order. Sometimes the entire starting row consists of creatures, in which case at least one player needs to buy some Heavy Infantry in order to deal with them. But then if loads of buyable stuff comes out, you need the Runes to be able to afford it. I like nabbing as many "draw extra cards" cards as possible - Master Dhartha, Ascetic of the Lidless Eye, and so on. That way I can burn through half of my deck in a single turn and sometimes therefore get to the bottom and shuffle the cards I just bought into the deck I now need to immediately draw from :D. Getting a good combo of as many Mechana Constructs as possible is really cool too, but can be difficult. It's nice to get hold of Mechana stuff anyway for the high Honour score (especially the Hedron Cannon, of course, with its value of eight, the highest in the game).
You can try the web client to get a better idea of Deck Building genre. The board game style is definitely better but this implementation is quite decent.
The key differences between Dominion and Ascension are two-fold.
Dominion has you randomly select a number of card sets that every one can purchase from, each set is difference but each card within a set is identical and everybody can purchase from those sets.
Ascension has one single deck loaded with lots of different cards, some cards are unique and some have multiples; you flip over x cards at the start of the game and a new card after someone buys one, thus the cards you can buy change each turn as the previous person buys them. It adds a very real 'screw you' component to the game.
The second key difference is that in Dominion buying the cards is the only win condition of the game, there are cards that are worth victory points and you can only acquire them by buying the cards and adding them to your deck.
Ascension has multiple ways to earn Victory Points. Some of the cards in the deck are worth victory points, some allow you to take victory points when you play them and some are enemies to be defeated that grant you victory points when you do (and those cards are NOT added to your deck).
Dominion leads to a much cleaner game, you can plot out a strategy from the beginning and work towards your ideal deck.
There are some edge cases that invalidate two of your generalizations describing Dominion, however. The first is both Knights and Ruins cards. Each Knight card is a completely different card (even though they are part of the same card set) and the Ruins deck has multiple copies of 5 or 6 different cards. Both of these are only available in the new Dark Ages set.
The other part is that there are some Action cards which give Victory Tokens, such as Bishop and Monument. When these cards are played, the appropritate amount of tokens are placed on one's Victory Token Board, and includes that count alongside any victory cards in the deck, much like how Honor pieces are counted alongside the Honor value of cards in one's deck in Ascension.
From what I've gathered, it seems like it will be dominion/thunderstone (got to throw that name out there, since its my current favorite deckbuilder) mixed with exploration. So instead of the stacks being all in one village, discovering a location would allow you to take from the cards there.