Here's a blog article on ER cooling in a trawler
Adventures of Tanglewood: Engine Room Cooling
In this case, the engine consumes about 1000 CFM of air, but a total of about 3000 CFM is needed to keep the ER at a temp rise of 20-25F. The extra 2000 CFM requires exhaust fans. That's continuous airflow while underway, not just when you shut down. Without it, the temp just climbs and climbs and climbs. If you are doing short runs it won't be a big issue, but if you run for 4-6hrs or more, let alone 24x7, it's a problem. It's hard on equipment, and downright dangerous if you need to spend any time in the ER fixing something.
As for intake vs exhaust, both will get the air out. Intake fans will pressurize the ER and push the air out through vents or other passages. Exhaust fans will create a vacuum and pull air in through vents and other passages. The ideal situation is with a bit more exhaust than intake such that there is a slight negative pressure (vacuum) in the ER. That prevents smells and heat from being pushed out into the boat through various unplanned paths.
In a boat with sufficient ducts and vents, there is no need for both intake and exhaust fans. Air coming in has to equal air going out. And with a desire for ER negative pressure, that means exhaust fans are preferred, and intake fans, if of matched flow capacity, will have no effect and are not needed. The only situation where intake fans will help is where there are intake duct restrictions that need to be overcome.
One other thing to not overlook is fan shutdown if you have an automatic fire extinguishing system in the ER. For those to do their job, they need to be paired with an engine shutdown system that kills the engines and fans if the fire system triggers. Otherwise, if the fans and engines are allowed to keep running even briefly, they will evacuate all the fire suppressant before it can do it's job.