Both sides use the same chain: measured fuel burn for the aircraft type at this sector length, multiplied by distance, multiplied by 3.16 to turn fuel into carbon dioxide, then divided across the passengers actually carried at an 83 percent load factor. Nothing here is modelled from first principles.
The per-passenger-kilometre figure is usually the more honest comparison. A long flight emits more in total simply by being long, so comparing a short hop with an intercontinental sector on totals alone tells you mostly about distance. Per passenger-km tells you about the aircraft and how densely it is configured.
Carbon dioxide only: contrails and nitrogen oxides at altitude roughly double aviation's warming effect, and the cabin split assumes a layout typical of each aircraft. The full method, sources and caveats are set out in how we calculate flight CO2.