Cheaper to eat out/cook, rather than all inclusive?

I was looking at Martinique and Guadeloupe as they have good prices for nice apartments to go self catering, but I am worried about the grocery prices as I see how expensive the food is on the islands.
I understand, that in general small, independent stores can be overpriced. But what about supermarket chains? Lets say, bread, milk, veggies, fruits, some seafood, soft drinks, wine, beer… nothing crazy 😀