I'm largely pulling from a video that Hyce published recently on the topic, that that there are several pros, cons and factors involved. Keeping a historically coal burning engine as original is definitely something a museum would like to do, but apparently as the world's coal power plants are shutting down, so are the mines. Modern coal plants burn coal that is ground fairly finely, steam locomotives prefer large chunks, so that's still a bit of a special order. Meanwhile it's fairly easy to find bunker C or used motor oil or even used cooking oil.

Firing a coal-powered engine is a back breaking exercise because the fireman IS the fuel pump, shoveling literal tons of coal from the tender into the firebox, but given the mass of the fire it is fairly automatic when responding to changes in throttle from the engine. Oil fired engines are a matter of turning valves, but without the mass of the coal bed a change in demand from the engine requires fairly swift action from the fireman.

Shutdown of an oil steamer is a lot easier, when you're done you close a valve, the fire goes out and she'll spend the next week cooling down to room temperature. With a coal burner you've got to extinguish or dump the fire, fuck around with ash, etc.

And, fires are a thing. Early in her heritage career, UP's Challenger just about burned down all of Utah. The state wasn't going to let them run it again without converting to oil. They had to do the same with the Big Boy for the same reason. Other heritage railways are making the move to oil firing because it's making more and more sense for 21st century steam traction.