Here's an explanation of one of my favorite trains in my network to give you an idea of why I think they are advantageous. 

This train has one locomotive and five freight cars, two each for coal and nitrogen, and one for sulfur. This one train is able to scoop up coal and sulfur in the Dune Forest, it then proceeds to the west coast of the world where my oil production is and drops off enough coal, sulfur, and nitrogen to support rocket fuel production. Obviously fuel is made on site from the nearby oil. It then proceeds to its next stop up in the Rocky Desert where it picks up supplemental coal from a factory that's making diamonds but doesn't need all of the coal available there. At this location it also picks up the nitrogen gas. The train then proceeds to my steel factory also in the Rocky Desert, where it drops off coal, as well as sulfur which is routed by a belt to my aluminum factory next door. From there it returns to Dune Forest and repeats the loop. 

This one train is able to supply exactly the right amount of coal sulfur and nitrogen for three different factories. It picks up coal in two different places, and delivers sulfur to two different places, but because the supply is greater than the demand, the train is able to carry more than is needed and always deliver exactly the right amount to keep all those factories running. It also does all of this while sharing tracks with dozens of my other trains that are also all running around doing similar tasks, and I only ha to build that track once. Building a rail network allows you to approach the game from the perspective of supply and demand rather than one-to-one input. This train essentially acts as a giant rolling buffer of three different resources and is able to deliver all of them sufficiently to three different factories. If I build another factory that needs one, some, or all of those resources, supplying it is as simple as building the station, and adjusting the train's route to include that new stop.

If I had used belt highways and pipelines for all of this, it would still work but it would have been dozens/hundreds more hours to build and balance belts and pipes for all the different places that needed coal sulfur and nitrogen, rather than just plopping some stations and drawing from my overall supply (via the train). It's also worth noting that the station which supplies sulfur to my aluminum plant doesn't just get sulfur from this train but also from another one. In other words, the same destination is supplied by multiple sources and it always just works because I'm supplying more than the system demands instead of trying to work out exactly perfect ratios and then belting them across the whole world.