Is it better to leave a child's skin scrapes covered with a band-aid or uncovered?

Wound care. Covering a wound does help protect against bacteria. And keeping it a little moist will help reduce scarring. A good general recommendation is to simply cover a minor wound with plain vaseline and a bandaid. If you feel you need an antibiotic ointment then just use it for the first day. However, vaseline (petrolatum) is just fine.
Covered. When i was a kid, the conventional wisdom was "leave everything exposed to the air." however, studies have shown that cuts and scrapes heal faster when they are covered. They will ooze more, but that's okay. Change the bandaid every day and keep it clean with soap and water.