In reply to the OP, I think this is a very tough question. I honestly feel that Dominion is the best game I've ever played, when it comes to that perfectly rounded balance of luck, skill and elegance.
There are games out there that are better than Dominion in some ways, but which are worse in others, and it remains my favourite game overall. I'll list the ones that beat Dominion in some ways.
First up, Chess. No, this isn't a throwaway silly answer, but a serious one. There's a reason why chess remains recognised as the purest and most brilliant strategy game in the western world. It has strategic depths that Dominion could never hope to reach, with complexity evolving from simplicity at fractal levels. Also, the more you study chess the more it challenges you. This is a rare thing to find, as most modern (by which I mean 20th century onwards) games don't give that: with something like Dominion, for example, I find myself less challenged by it the better I get at it.
Second, Vampire: The Eternal Struggle. While I love Magic: The Gathering, I've always considered V:TES to be the pinnacle of CCG design, especially when played in the five-player format within a tournament setting. Given your opening post, you may find some elements of V:TES distasteful. Because its a game where you bring your preconstructed deck, its not always fair. Even though it has an attack-left mechanism, its still a game where you can be ganged up on and where a weaker player can commonly play kingmaker. The beauty of V:TES, however, is that the thematics and the design all make the vicious free for all into a design feature rather than a bug. You're not at the mercy at the random whims of your opponents: rather, its by manipulating the balance of power and by trading favours and promises that you truly master the game. The game rewards those who know how to tabletalk from a position of strength or weakness, and who understand the dynamic of the shifting pressures of force and threat.
Third, the Descent board game. Is it balanced or strategically deep? Hell, no. Well, not compared to something like Dominion. But short of an actual roleplaying game, no game I've played gives me the sensation of fun and of walking in my character's shoes. I have more fun playing Descent than Dominion, even if I recognise that from the point of view of elegance and depth of game design, its not really that clever.