I've recently been thinking of adding a wargame to my collection and both A Game of Thrones: The Board Game (now Second Edition) and Warrior Knights are interesting choices.

If you were to pick one of the (and only one), which would it be and why?  

 I can't tell you about a Game of Thrones, But I can tell you my personal opinion of warrior knights. Warrior knights is a great game with a few friends (I find it better with 2 or 3 other people) and it's not a game where you press your luck, you actually have to think about your choices. Want to keep conquering cities and kill other nobles? well if they're worked to much, they'll ask for their payment. Keep gainig political influence and effecting the laws in other ways? There will be a meeting to decide on the laws of the Kingdom. Or do you want to walk out of the meetings, being immune to the laws but having no political power? Perhaps you should pay for a voyage on a trip to china, and hope you receive your money quadrupiled? Or does having the power of the church interest you? 

Warrior knights is a great game because of choices like these, your always thinking, but you'll never get "Anylisys Paralysis", or in other words think to much to slow the game. Also the game is as fast or as slow as you want it to be, as you can always lighten the win conditions. and of course, attacking or making "deals" with your fellow nobles is fun as well, and betraying them even funner, for it's all about you in the end isn't it? Random events will happen and hurt you, or sometimes you'll have your troops killed, but I've never had a warrior knights game where somebody was crippled in anyway to continue. Your always a participant in the game, and always having fun

   Sorry for the long post, but I hoped it helped.

Warrior Knights has one advantage - it requires less time and less people.

AGoT is made to be played by 5-6 people (at least the 1st edition), relying on backstabbing game mechanics and thorough planning, seeing how there are no dices in the game and almost no random factors. But on the other hand, more than once we hunched over the board for 5-6 hours, thinking and rethinking our next moves.

The 2nd edition of AGoT is better, fixed some problems and included all six Houses in the game, no need to buy expansions (yet).