Chiana Dickson, Homes & Gardens' junior writer and DIYer says that either will work, but satin is easier to clean. When painting a kitchen, it is more important to have specialized kitchen paint (or bathroom paint) that stands up well to moisture to prevent mold growth and peeling paint.'
With proper preparation, priming, and quality paint, eggshell or satin will be durable while bouncing light around and making cleaning the kitchen easier.