Nitrogen for filling tires provides very limited benefits. The ONLY practical one is that it is more reliably dry than the compressed air that you would get out of a typical filling station. The other claimed benefits, like having a larger molecular diameter, having less mass per molar volume, and being less reactive are all true but make VERY little difference in actual use in a tire used for normal conditions, even for racing.
The reason they use nitrogen for aircraft tires and for racing vehicles is because the expansion characteristics are less extreme and more predictable if the interior of the tire does not contain any liquid water. That is a really big deal for aircraft because they and the tires move from moderate temperatures to very low ones while in flight to very high ones when they touch down. The same feature has an impact for race cars but they usually don't get to the very low temperatures. But in both cases air would work just as well if it is kept dry.
I'll skip the lecture on why it's difficult to get dry compressed air and why it's more reliable that you will get dry nitrogen.
Anyway, the other claims are
true but they don't provide any practical benefits. Tires were designed to be filled with compressed air. Yes, the N2 molecule is about 10% larger than the O2 molecule but the rate of pressure loss for air is still very low. Check the pressure in your tires regularly and either gas works fine. Yes, N2 is far less reactive than O2 is. But while O2 at 100% is pretty scary, it is pretty tame at 21%. Unless you expect to keep your tires for a century, the internal surface of the tires will look almost new when you replace them. Yes, N2 is lighter than the same volume & pressure of O2 or air (2.9% vs air), but the mass of air in a tire is 0.05 lb (22 grams) versus 60 lb (27 kg) for the tire plus wheel so the difference will not change the unsprung weight of the tire.
Unless your bike, car, SUV, or airplane is going to be going from frigid to hot temperatures in a matter of minutes - just use air and check your tire pressure regularly. You will have no measureable difference in performance, fuel efficiency, or tire life.
But you can get those eye-catching green valve stem caps if you pay for the nitrogen.
Yes - I'm a scientist, and you can probably tell that I get annoyed by pseudoscience sales claims.
Chris