As RPS describes it, "Eurogames are the board games you can play in polite company" and "If you’ve ever rolled a dice to hit the guy sitting to your left with a poisoned lance, causing him to storm out of the door and march back to his mum’s house with tears in his eyes, you’ve played some prime Ameritrash."
Tobold feels that Eurogames are a much more popular genre than Ameritrash. But I am not so sure.
First, let's get rid of the prejudicial names. I observe that there are two main styles of adversarial games: Last One Standing, and First to the Mark.
Last One Standing games feature people being knocked out as the game goes on. The winner is the person who survives and defeats all her opponents. Examples include Monopoly, poker, Axis & Allies, and Diplomacy.
First to the Mark games usually feature everyone gaining score, with the winner being the first person to reach a predetermined state. Examples include Settlers of Catan, Clue, and trick taking games like whist or euchre.
There's also a third type, High Score at Time. But these games are often just one of the other two types with a time limit. If you remove the time limit, it's often pretty obvious which category they fall into. For example, Risk is a Last One Standing game, only with a time limit. Scrabble is a First to the Mark game with a time limit.
As you can see from the examples, it is not at all obvious that First to the Mark games are innately more popular than Last One Standing games.
I think that both game types have strengths and weaknesses. To me, Last One Standing games are often better when the stakes are higher. Poker dominates the other card games when it comes to gambling. On the other hand, Last One Standing games are very annoying if the elimination period is very long. It's no fun being the first person knocked out when the game continues for a significant period of time. As well, two people can often team up against a single other person, and the out-numbered person can rarely survive.
With First to the Mark games, everyone usually gets to keep playing the game until the very end. On the other hand, one thing I loathe about this type of game is the presence of kingmakers. Kingmakers are players who absolutely cannot win, but can determine which of the two leaders will win the game. Often times, a kingmaker's support will have nothing to do with the game, but much to do with outside relationships.
First to the Mark games are also less adversarial than Last One Standing games. A lot of people might say that this is an advantage, but I am not so sure. Many times, First to the Mark games don't really feature a lot of interactivity between the players. It's like each player is playing solitaire, and the fastest player wins.
In more interactive First to the Mark games, negative interaction comes in the form of "refusal to help". Somehow I find that an outright attack in Last One Standing game is just more honest and less frustrating. An attack is what one expects. Maybe it's just me, but I take getting attacked in a wargame--or even getting betrayed in Diplomacy--much better than someone refusing to trade in Settlers of Catan.
So both types of games have strengths and weaknesses, and I think it is incorrect to say that one type is obviously better or popular than the other. But one thing is that Last One Standing games are best when they reset quickly, and that is often against the nature of MMOs.