Subsidies and externalities kind of muddy the water when it comes to ticket prices. While it is generally cheaper to fly, this is because you are not paying for the damage your flight is causing to the city around it. Noise, pollution, damage to property, and disruption of the quiet enjoyment of those around you.
Shinkansen is a for profit business that acts as an engine to turn worthless rural land into extremely valuable land. Air travel does the opposite. Property values around airports are extremely low. Every plane rattling people's windows and dropping a plume of unburnt fuel and exhaust on people's heads damages the area under it.