The Ringed City improves upon Ashes of Ariandel in pretty much every single way. It's longer, contains many new enemy types, equipment, interesting lore and the final boss is one of the best fights in the entire series (you can probably tell who it's if you have played the first expansion).
I would suggest buying this as part of the Deluxe edition, but it's good enough to be bought on its own during a sale too.