For one person travelling light, a rail ticket will usually be the cheaper headline number. The comparison changes quickly once you add people. A taxi fare is charged per vehicle, not per passenger, so two, three or four travellers split a single price while rail tickets multiply. Add the cost of getting to the station at either end, and the gap narrows further. The other half of the comparison is not financial: a fixed-fare taxi removes the connection, the luggage handling and the timetable dependency. For a family with cases or a 5am departure, that is usually the deciding factor rather than the fare itself.