The advantage of a tire filled with an inert gas versus atmospheric composition is that it is less susceptible to pressure changes due to expansion/compression of the gas inside the tire/tube due to temperature changes.

I believe the Space Shuttle has its tires filled with an inert (I believe it is N2) due to the extreme temperature changes from space to earth.

100psi is 100psi, no matter if is air, nitrogen, oxygen, etc. But, each of the gases (or compounds as in the case of the atmosphere) is subject to different characteristics at different temperatures and/or pressures.