Collard greens belong to the cabbage family. One of the milder greens, the flavor is somewhere between cabbage and kale. Selection: Choose smaller leaves for tenderness and milder flavor. Look for fresh green color and leaves that are moist, crisp and not wilted. Storage: Wrap unwashed greens in damp paper towels. Refrigerate in a plastic bag, in the crisper, up to 5 days.