I've had very limited experience firing oil burners, but do agree you have to watch very carefully what the engineer is doing or you'll get behind in a hurry. Not noticing the engineer has opened the throttle can lead to your fire going out from the increase in draft. Not noticing your engineer has shut off will lead to huge clouds of billowing black smoke.
I have five summers experience with coal on the C&TS. One trick about coal is you have to anticipate a change in steam needed (for example the change outside of Chama encountering the 4% grade) as coal takes a little time to burn its hottest. Same thing applies when leaving the yard: I used to put a large fire in the engine about 3 minutes before highball and it would just be ready to go when we got the signal.
The biggest challenge for many coal firemen is keeping your balance on the shifting deck, while stamping on the clamshell door pedal, and slugging the coal exactly where it is needed. Usually, the ballet ends up with the door open at the right time and the coal headed for the right place in the firebox, but on occasion the door didn't open in time and the fireman was rewarded with the jarring impact of his scoop with the still closed door and coal flying all over the cab (even bouncing off the engineer-who dislikes this intensely). Or the coal would end up somewhere not needed which means you have to put another scoop in. Some of the engines were very tempermental about where they wanted the coal: The K-37's loved a good deep heel around the front and sides of the firebox and it took quite a wind up to get the coal to the front of the firebox. I knew firemen who hated the #497 as they were over 6 feet tall and couldn't stoop low enough to sling the coal properly to the front so it would never steam well for them. #497 was one of my favorites because you could be down about 5 lbs of steam pressure and a couple of good scoops in the cold spots would get the pressure up again in a couple of minutes. The K-36's were very good steamers which liked their coal in a heel around the back of the firebox. They generally all steamed well and if you got behind you could get caught up again by a little extra work in about 5-6 minutes. The K-27 #463 was very tricky. It liked a heel in the back, BUT only a very thin bed of coal in the front as the arch came down very close to the grates. Slugging too much coal into the front would stifle the draft and it would quickly lose steam and then you had to work extra hard trying to get your pressure back. #463 is the only engine I ever had to rake a fire while underway to get it back to steaming effectively. As long as you kept on top of it and watched your fire carefully it would steam OK.
I've had really no experience with wood burners, but can tell you from riding in the cab of the Eureka that the fireman never really sits down as he's constantly putting wood in, or going back into the tender to gather more wood to put in. George Sapp has fired the Eureka on many occasions and he says he usually has a couple of pieces of wood in his lap at any given time that are about to go into the firebox. Dan Markoff usually has at least one other person in the cab who's sole job is to pass wood to the fireman. It would be a helluva job for only one guy with no helpers!
It's easy to see how the forests were clear cut in the age of wood burning machines...