I've only played Magic twice, my friends begged me.
To me Magic makes no sense. I mean this because the world of Magic was not a coherent, unified, and well-known place, at least to me. But the world of AGOT card game is well known to me... and I get a thrill when the Kingslayer and the Blackfish face off. In Magic, when my clay golem fights my opponents goblin horde there is no sense of wonder... I don't relive an epic story... to me it's meaningless. I'm not into Magic for the sake of generic fantasy, I like my fantasy grounded in reality.
All that said... I think AGOT is brilliant. It is played on three levels... Political Power, Military Power, and Intelligence (espionage) power. You can try to balance your deck or steamroll your opponents with a single type of attack. Obviously the Lannisters specialize in espionage, the Baratheons in politics, and the Greyjoys in military.
On the board you have characters and locations. Characters allow you to attack or defend. Locations generate income or give special bonuses.
Each player goes in order of initiative which is determined from his/her agenda card played each turn. The agenda card gives initiative, an income, and a condition to affect you or your opponents... sneaky, sneaky.
I have about four thousand cards. You make decks according to the great houses of Westeros. I have many playable decks... in fact I make my decks from the books, I don't just make power decks. I mean, Jon Snow should not be in the same deck with Cat, nor should Bronn work with Cersei. My decks are Robert (support from all houses), Stannis (Asshai and Pirates), Renly (Knights and Tyrells), Tywin (Armies, Ambassadors, money and Jaime), Cersei (Spies and Jaime), Tyrion (Clansmen, whores, sellswords and Jaime), Dany (Dragons and Queensguard), Viserys (Dothraki, it's a "what if" deck), Balon (Longships), Theon (Longships), Oberyn (Sandsnakes), Robb (Armies and Tullys), Ned (Winterfell), Night's Watch (Jon), and Wildling (Mance).
The game is usually played by two people, but is a real blast when playing with three, four, or five people.
When you play the game of thrones, you either win or die.