As for direct GHG emissions, the most efficient mode of travel depends on many factors involving the models, occupancy, and route, but generally speaking, planes can become more efficient than trains for distances >= 700 miles.
Turns out motor coaches (e.g. Greyhound busses) are the most efficient at pretty much any distance.
Germany's department of environment number for travel by rail: 38 gram/kilometer = 0.13 pound per passenger mile.
(Source (German): https://www.vcd.org/fileadmin/_processed_/8/9/csm_Emissionen...)