I choose Stanley barely over Olympics and then Championships.
I think the tournaments are really great and I'm usually very proud of the guys. I also get to see a few players we never see in the NHL, which is fun.
But Stanley is a 2-month grueling war following a tough season. There is usually a lot of drama, a lot of history, sometimes bad blood. It's a slow buildup which makes the resolution all the more intense and interesting.
That's the difference.
Tournaments are very short time. There are also more often mismatches. And a single bad game can ruin it for you. In the playoffs, you can make mistakes (and thus enhance the drama) and then redeem yourself. THAT is what's cool.
You can see the emotion on the players' face. If you've won the Cup, you've worked extremely hard to get there.
But I still love international play.