3 big reasons from my experience:
1. When it comes right down to it, we don't fight fair. We have an attitude that says if it is not strictly forbidden then it is allowed. That gives the average American soldier/sailor/airman/marine a decided advantage over 99% of the world's military forces, because we are able to think, be creative and find a way to outgun, out maneuver or out think our enemy. Where we can, we get that technological advantage. If they have it, then we quickly find a way to negate it. When we find that advantage we use it for as long as we need to use it--but no longer.
2. And that points out the other big advantage--American's have the ability to go all in for as long as we need to to achieve an objective, and then quit in a heartbeat when the situation changes. An example: In Afghanistan we had captured a 12 year old kid in a fire fight and were trying to repatriate him to his village. When I talked to the SF team (well, the 4 who had been in the fire fight) to see if the kid was a threat I found that they had shot 7 of the 8 enemy during that fight, but had not shot the kid because they all saw he wasn't really a threat. Few Armies on the earth now, or in history have that kind of mindset that allows even the lowest ranking soldier to have that level of situational awareness and confidence in their ability to make crucial decisions in the heat of battle. Yes, our training is 2nd to none, but that mindset makes a huge difference.
3. In the end, we are all Americans which means we are part of an egalitarian system that once you put on the uniform it really doesn't matter where you've come from, it matters what you can do and whether you do it. Sure, there are examples of wealthy kids buying their way out of Viet Nam, but there are also examples of rich and famous men and women giving their all and even more who simply served without fanfare. I've met too many rich men in other Armies who wouldn't pick up a shovel to dig a trench, but those who had U.S. on their chest would do that and more.
Ok, my nickle is up.