Their players care more about winning the Ryder Cup than our players do.
Just go down the list of the matches on Sunday and ask yourself, which player cared more about winning?
Phil Mickelson, or Justin Rose?
Bubba Watson, or Luke Donald?
Francisco Molinari, or Tiger Woods?
For the Europeans, the Ryder Cup is their #1 career highlight. Some of them know they'll probably never win a major championship, and even some of the ones who have, or might, think the Ryder Cup is a bigger deal.
Some of the Americans say it's just as important to them, but I don't believe them one bit.
P.S. One other factor: European golfers have more access to golf in the modern era. They had to deal with reconstruction after W.W. II for many years [not to mention they probably lost some potential champions in the war]; and even after that, economics and a lack of golfing culture on the continent held them back. It's only in the last 20-30 years that golf has become popular there. You can attribute a lot of that to Seve Ballesteros, who came 25 years later than Arnold Palmer did the same for Americans.