I use both! Air contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide... and it's free.
Air from your compressor comes with water vapor which condenses under pressure....hence the blow out of liquid water when you open the valve at the bottom of your compressor tank. Once that water is in your tire, it will transition from liquid to vapor as the tire temperature is increased and the tire pressure will increase more rapidly.
Nitrogen (from a gas cylinder) is essentially free of water. However, if you don't evacuate any water liquid/vapor already in the tire, you don't get the full benefit of the money you spent.
You could do the same thing with any pure gas (with b.p. << ambient temp.), but ideally you'd want to pick something like N2 that is inert and cheap. Otherwise an inline desiccant would filter water vapor out of the air from your compressor, but might not be any more cost effective.
well... as a streetbike, my CBR will never see huge pressure changes because it will not have a large tire temp change....
and since its pressure is not only checked regularly, but also since the tires rarely last me more then a couple months...... Nitrogen is worthless to me.