I have nitrogen filled Michelins that I purchased at COSTCO. They fill all tires with nitrogen and refill if necessary.
Keep in mind that about 3/4 of the the compressed dry air in your tires now consists of nitrogen, about 1/5 is oxygen and the rest is a small amount of other gasses. So when you get a fill of only nitrogen, you are only displacing about 20% the total air in the tire with nitrogen. Why nitrogen? It is an inert gas that has larger molecules than oxygen so seepage through the tire is considerably less. Nitrogen also does not support moisture.
As Turtle mentioned you get Smoother ride, stable inflation, better fuel economy, longer tread wear when Nitrogen is used.
I think the reason you get all of the above is only because stable inflation maintains the ride you desire, smooth or hard. Stable inflation at recommended pressures also gives you better fuel economy and improved tread wear. This all could be most important on dual wheels where stable and equal pressures on each tire are essential for fuel and tire economy.