You can use them both. For kitchen wastes, get a 2-gallon plastic bucket with a lid, drill a few holes in the bottom and stand it in a plastic tray. Mix the kitchen wastes up with about the same amount of dead leaves or more, and put it in the cardboard box. Add more dry stuff on top. Close the top flaps.
Mixed ingredients are better, add a small handful of soil per bucketful.
You can add any garden wastes at the same time. Leave them spread out somewhere dry to wilt until you're ready to empty the kitchen wastes bucket. When the first box gets full, add the second box, taping the bottom flaps over the opened top flaps of the first box. When both boxes are full, start a new unit with two new boxes. After a couple of weeks, tip the first boxes over, empty them, mix everything up evenly, add more water if it's too dry, and put it back in the boxes again.