I was a kitchen table player in high school. I've played a bit recently online but not with any consistency.
As far as similarities, well, they're both played with cards. Other than that, they are quite different. While I was introducing my wife to Dominion (who I had previously tried to introduce to Magic, unsuccessfully), about half way through the first game she said, "Oh, so this really isn't like Magic at all." I laughed and said no. She likes Dominion much better.
The most interesting difference to me isn't the game play but the ability to play the game casually. Magic is much more fun to play casually because the cards are just so cool. The universe is compelling and summoning giant monsters to smash your opponent's face is fun, if not the winningest strategy. Dominion's flavor component is not nearly as developed as Magic's so it's not as enjoyable on that level. And it's not just the depth of the theme but the way the theme is connected to the mechanics of the game. It's not enough for "Vampire Lord" to have a picture of a big bad vampire on it. What it does in the game must also feel vampirey. Dominion cards don't achieve this on a consistent basis. Pirate Ships steal treasure then give you coins. Sure. A black smith draws cards? Huh? A village gives you actions? Wait, how is a village even an action in the first place. Isn't a village a thing?
But that's ok. I play Dominion for different reasons than I play Magic. I like that I can play Dominion at a high level (not that I'm there yet) without a huge investment in time or money. I like that I can introduce Dominion to a new group of people and have a fun night of gaming without a huge learning curve.
