The theory behind nitrogen in tires is that the nitrogen molecule is significantly larger than the oxygen molecule. Nitrogen "generators" simply take out the majority of the oxygen from the air leaving 95% or so nitrogen to fill the tire. (air has roughly 78% nitrogen and 21% oxygen)
So in theory the larger molecule will not leak out of the tire as quickly as the oxygen molecule. Race car and aircraft owners and the military have believed in nitrogen filled tires for years. Virtually all vehicle and tire manufacturers recognize that tires do leak down over time and all recommend that you check and adjust the inflation pressures regularly. Optimum tire life and fuel mileage is obtained with proper inflation. If your tires never leak, congratulations, virtually every tire loses air.
Oxygen leads to oxidation. Whether you call it tire rot, or any other name, oxidation is slowly degrading the "rubber" and the steel in your tires. All tire compounds have some amount of porosity, tiny little holes that gasses can permeate. The gas used to inflate your tires is under pressure, up to 110psi or more, and will migrate thru those holes into the steel belts and eventually out of the tire. Nitrogen filled tires in theory do not oxidize as quickly as those with oxygen in them.
Depending on your wants and needs you might want to consider nitrogen in your motorhome and trailer tires. Those who depend on their tires, race car and airplane owners and the military obviously think the idea has merit. Not all tire stores charge extra for nitrogen. Typically tires filled with nitrogen have bright green valve cover caps. Is it worth paying for nitrogen? I guess that depends on whether you believe in the theory.