It wouldn't make any difference. Most gases behave as ideal gases at the sort of temperatures and pressures we use them at - so oxygen and nitrogen expand the same for a given temperature difference - so if the tube overpressures with air (78% Nitrogen anyway), it will also overpressure with Nitrogen.
The advantage of Nitrogen is that it is dry (from a bottle) and oxygen is needed to oxidise stuff - so the water vapour and oxygen can't react and corrode inside the wheel/tyre. Supposedly, the oxygen molecules are smaller, so are more likely to escape through the tyre walls etc - so it needs topping up less often - but that sounds a bit tenuous to me - marketing spin anyone?!?
And on the basis that the only advantage is that it's dry - I can't see how it makes your tyres last 25% longer either.
It's yet another way for garages to charge a few extra quid for not a lot.
However, Nitrogen is just a teeny bit lighter than Oxygen - so it might effect your mpg - but to put it into context, if you made sure that you went to the loo before each journey - the difference would be much greater!!