In my search for Shimonoseki - Busan, it was like 171.13 USD for a round trip. So bit cheaper to book directly.
Lastly, I checked tripadvisor for flight tickets.
Since I believe this is for the cheapest option and not about the destination, I changed the location to international airports (Fukuoka - Seoul) which will likely have more flights, hence likely be cheaper.
At the time I searched the cheapest for Fukuoka - Seoul was 11403 yen for a round trip, so seems in a given situation, the chances are that flights could be cheaper.
JFYI, ferry takes like 8hrs, flight takes like 1hr 25mins.