Heat-cured acrylics are less porous, harder, easier to polish, easier to clean, and generally last longer. But, they have to be processed in a laboratory (generally).
Self-cured acrylics are quick &easy to use, so a dentist can use them in a clinical/practice setting. You don't have to send anything to the lab and wait. Large projects = heat-cured preferred. Small projects = either is okay.