Like the others said, it makes next to no difference. Here are the claims:
1-Less loss of air. Minor plus, tests show a very slight difference over a year, you should be checking tires every month, anyway.
2-Better economy. Nonsense, both nitrogen and air act identically as far as mileage is concerned. Only reason someone might think it's better is because they're finally paying attention to tire pressures.
3-Better ride. Nonsense, again, given equal pressure.
4-Race cars/airplanes use it, so it must be good. Not true for us. Race cars use it to precisely control pressures to the fraction of a psi, not something we do. Airplanes use it to eliminate a potential fire hazard (high pressure air).
Major downsides are cost (not worth a dime), and the problem it creates keeping tires properly inflated (not available many places).
2

0
