Efficient, how? It uses much more energy, makes more noise and creates more pollution.
The speed has very little to do with the funding model. Flights were still faster in the 1970s when many state-owned airlines operated, and trains are little different when private companies run them (see: several European countries).
Planes also spend their time where there is less wind resistance to deal with.
Trains are still a win, but it isn't as clear as it seems.
I'm not sure what noise has to do with efficiency - I doubt that the energy expended on vibrating the air is physically or economically significant - but it is worth noting that trains are loud. Particularly because regulations written in blood require that they blow their horns three times at every level crossing at all hours.