Both dramas are light dramas, there's not much angst
Both female leads are cooking prodigy, and of course we get to see A LOT of cooking and food, up close and in slow motion
Similar title, both center around food and the bond that grows between two people. In MD, the FL has an eating disorder, and in DD, the ML is very picky about food.
Both are historically set and a love story between an emperor or prince and a female chef. Both feature many scenes of cooking and eating various dishes.
Both FLs are upbeat personalities, while the ML is more stoic and in a higher position in some way (talented chef vs. emperor). Both dramas have a some romance and cute scenes between the couple but the main focus is on the food, with many delicious shots of cooking/food preparation.
Both dramas are set in the palace in historical times, with an emperor ML and a FL who is very talented in cooking. Both are lighter, enjoyable dramas.
Despite the different settings, both are historical and have similar elements - the ML is in a position of higher power, the FL is a servant who cooks for him and his family, and the two initially have a bickering relationship.