Nitrogen has better compresability, mor rather less compressability than air, about 20%, since air is ~80% nitrogen. Now CO2, is even better........
I would think that any benefit from lower oxidation, leaking, or thermal effects would be so minimal that it is not the main goal. Lower compressibility means less dive in cornering due to the tire compressing and distorting the relationship of tread to the road surface, meaning better handling. This factor is the basis for all gas shock absorbers, too, and would guess that it makes a difference with aircraft tires, also.
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'89 245 Sportwagon, '04 V70 2.5T Sportwagon