For the Herschend route: I would expect them to treat Kings Island as one of their premier parks alongside Dollywood and Silver Dollar City. Here are some of the things I could see happening:
New (old) logo to differentiate itself from its former Cedar Fair / Six Flags ownership, either reusing the first logo or coming up with a brand new one altogether
Kids area removes all the Peanuts or Looney Tunes IP and is rethemed to something similar to Wildwood Grove or Discovery Meadow (Phantom Theater stays as-is)
Cinnamon Bread location added somewhere in Rivertown
Trams could possibly return to the parking lot, as they're still used at Dollywood and SDC
The park adds more family attractions, since that's the market Herschend wants to appeal to the most. It would also help differentiate it more from Cedar Point up north, which would still be owned by Six Flags and catered more to thrill-seekers
Either a new resort gets built to attract non-locals, or Herschend buys the Great Wolf Lodge next to the park and converts that into a new Kings Island resort
Action Zone gets rethemed to an all-new theme from Herschend, maybe an expanded Oktoberfest section as a way to celebrate Cincinnati's german heritage
All of this, however, is completely hypothetical. I don't expect Six Flags to sell off Kings Island considering its one of the chain's top parks. I also don't know if it would be good for Herschend either, since they just tripled their park portfolio due to the acquisition of the Palace parks. It's still fun to speculate on, though!