I think it is different for the type of wound. When Bella had a horrible ulcer we tried it both ways. When it was moist it looked awful, when it was dry it looked clean. The optimal wound healing for her ulcer came when the site was free of bacteria and was debrided with the saline mist therapy treatment. It healed right up when it was kept moist but only after it was rid of bacteria.
Standard rule for a cut or abrasion is to clean it well, apply an antibiotic ointment for a few days and the keep it clean, dry and open to air. I am so glad it all worked out! There is nothing worse than a wound.