Paul Krugman (who famously models transportation as an iceberg (and he got his "Nobel" prize in economics for his work in spatial economics and trade theory, showing how aspatial the field is in general), writes about: Trains, Planes, and Automobiles.
There are several problems with this image. First it assumes you are already at the train station waiting to board, as opposed to somewhere randomly in the region. Remember most people do not work or live downtown (even in New York City). Second it ignores the third mode of the title (automobiles). A redrawn figure, which is standard in transportation economics or geography, is shown below. [Similar graphs apply to freight, just change it to Trucks, Trains, and Ships]. The question is whether there is a range between d1 and d2, that is, does rail actually dominate both autos and planes over any region. In terms of travel time it probably does, and looking only at operating cost, it might. In terms of overall cost, including the fixed cost of construction of a new HSR line, it probably does not under current cost structures. The size of this range, if it exists, is, however, empirical, and subject to change with costs and technologies.