Nobody's replying so I'll give a crack at it.
No mention of destination so I'll just give an example for Shimonoseki to Busan (Korea).
Below is the web page of the Shimonoseki Port.
下関市港湾局：国際フェリー・RORO航路のページ
Doesn't show prices for all the ferries, but 関釜フェリー has their cheapest room as 9000 yen (one way).
I also checked the website below which is a ticket booking site for ferries.
Direct Ferries
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.
Cheap flights to Seoul (SEL) - TripAdvisor
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.
