Oh boy, here we go... bring in the chem-geek
Ok, yes nitrogen molecules are "smaller" than oxygen molecules by roughly 2 picometers (1 pm = 0.000000000001 m), so we're not talking about a big/significant difference. Certainly not the scale that is shown on the above mentioned website (which interestingly enough is sponsored by a tire company). Where the difference lies however is that Nitrogen molecules are "lighter" than Oxygen by about 13%, which is a significant difference. What that means is that Nitrogen will move significantly faster than Oxygen, which will make it diffuse (read: leak) faster. So first off, Nitrogen tires will actually leak at a faster rate.
Next, the website states that regular air is 1/5 (20%) oxygen. Totally not true. "Air" is roughly 78% nitrogen, but the remaining stuff is composed of a mixture of oxygen, carbon dioxide, argon, helium, hydrogen, and a whole bunch of other stuff. My point? The remaining 20% is NOT oxygen. Oxygen will cause the tire to oxidize ("corrode"), which does make filling tires with pure nitrogen seem a good idea, so tires won't break down as fast. But think about it... the outside of the tire is still exposed to oxygen, and how many tires have you seen breakdown from the inside out?
Third, per unit volume nitrogen (28g/mol) is "heavier" than water (18g/mol). Since air has a high moisture content, for those of you who will say that getting rid of the water is good, you're replacing the water with something heavier. This creates more rotating mass, which makes you slower to accelerate, and harder to decelerate.
Fourth, if you want to talk about gas expansion, at the temperature and pressures we are dealing with the non-idealality of the gases is negligible. In other words, since we are dealing with relatively low pressures and temps, the amounts of expansion per unit volume between nitrogen and "air" will be pretty much the same. You would see a big difference if we were near the melting/freezing point of one of the substances and not the other. That is not the case here. Nitrogen is at -210 C, and Oxygen is at -218 C.
Finally, the pump that you use to put "air" in your tire pumps in about 80% nitrogen (free). You're paying a crap load of money for that extra 20%, which I’m willing to bet you will not see a 20% increase in efficiency. Is it really worth the money? Are you really going to "tell" the difference? You may think it's "better for the environment", but have you thought about what has to be done in order to liquefy the nitrogen in the first place? I'm not saying it's bad, but most people hear about a new environmentally conscious procedure and sign up whole-heartedly before looking into the steps that lead up to the procedure to see if they are also "better".
Oh yeah, and in case you think I'm spitting random crap (I have said this before but) I do know what I'm talking about here. I have a degree in chemistry, teach chemistry, and right now I'm working in a research lab at the University of Rochester in New York along with 3 chemistry PhD's, 2 chemistry masters degrees, and 1 chemistry post-doc. And we have been talking about this one for a while... mainly laughing at the people who think this actually works.
Ok, I'm done now... feel free to flame if you feel the need, but I'm just trying to shed some valid light on this subject.