N2 is a gas and expands with temp changes just like any other gas.
Air is ~80% N2.

The advantage is that bottled N2 is dry and has a predictable expantion rate.
Normal shop air is not dry; as a result you need to take into account the water vapor content when determaining how it expands with temperature. Unless you know the exact humidity of the air you can not do more than guess.

Race teams use it because they know they will get X psi for Y deg. A change of 2psi can have a noticable affect on the cars handling.

On the street you should never be pushing the car hard enough to notice a difference.

If an N2 fill is free, go for it; if not, don't waste your money.

NOS is quite different from nitrogen.

Well I have checked and Nitrogen expands very little if that. We use it in go-kart racing, which the tires are very small, and a 0.5lb rise in pressure can make a big difference. When using regular air we see that there is a difference. When using nitrogen, there is no difference between cold tires and hot tires.



Also since the nitrogen is dry as mentioned before, it is also good to prevent corrosion on the inside of the rim, not a very common thing anyhow though.