The braking systems would largely have been the same between steam and diesel locomotives, so a significant portion of their train handling skills would remain applicable. Applying power on a diesel is a relatively simple process, the main concern being to make sure the traction motors were not being overloaded and not slipping. I would suspect a seasoned steam loco engineer would likely make the transition relatively easily.
One new feature of diesels without a corollary on steam engines was dynamic brakes, but relatively few diesels during the transition were so equipped. Those became more prevalent in 2nd generation units.
The person whose job changed the most was the fireman. They went from a demanding, physical job to mostly being a passenger.