I would go with the AB. The only time your parents will need to use the inside room is to sleep and change. Having the large living/dining room as shared space will be perfect. Throw in the perks, butler, consierge, Cagney's, Express on and off the ship, VIP cocktail party, perfered reservations......will make the trip special
The sofa bed makes up into a true double bed. Have the room stewards put a foam topper on it and your parents will be very comfortable.
As posted you may have to share some of the master closet space with the parents. Clearly it holds more then 6 items with 2 one foot hanger holders.