I think the Dodgers will. Ohtani is the closest thing to an NBA superstar where fans regardless if they are Dodgers fans or not will buy his jersey or merchandise. The last player who had a following like this was Trout and before that it was Griffey. MLB typically doesn't have these types of players because it is more of a local market only unlike the NBA where it is mostly a player driven market. The NFL also doesn't have an Ohtani or a LeBron like phenom where consumers will buy a players jersey and don't really follow the team the player is playing for. MLB, NFL and the NHL are all local market driven as there are very few to none where you will have someone or multiple players be their own market.
So I believe the Dodgers will definitely make a lot more off of Ohtani than they will of Freeman and Betts. It is possible Ohtani could reach just general Dodgers merchandise levels. You can't look at it as just Dodgers fans buying Ohtani merchandise but also non Dodgers fans which as I have stated previously is usually not the case for MLB teams. Ohtani is just in a different class than any other player in MLB right now. The only one who rivals him is Trout and he isn't even close to being on the same level as Ohtani is.