What colour is your trim? You want to make sure the whites play well together. My advice is to test out the whites on paint canvas boards (inexpensive 5 x 7 ones from the dollar store) and move them around the space throughout the day to see how they play with the light. Check the colours in your artificial light as well.

All that said, I wouldn't be tempted to paint your cabinets. I think once you paint your walls, you might find the kitchen lighter and the wood a nice warm foil for the black counters. Wood cabinets have been "coming back" for a while now. I'm seeing them often paired with white walls and touches of charcoal and matte black. (Painting cabinets is a huge job so rarely my first inclination in a kitchen. Optimizing the lighting is the first. If you don't have under cabinet lighting, consider adding some.)

Just my general opinion. I'm not a pro nor can I see the state of your cabinets in your picture. Painting cabinets can certainly transform a space and since you have an island, you might want to consider painting the island and keeping the cabinets wood or vice-versa. You have options. Taste, budget, energy and time are what determine the scope of a project. Good luck with your decision! :)