The curve of the flight of a ball depends on gravity - so the ball would go much, MUCH further because of the low gravity. But, it would land - not whiz off into space - because you can't throw it fast enough to escape even the moon's gravity. It would be fun to try it some day.
If you throw a ball on the moon, it never stops bouncing. There is significantly less gravity on the moon than on Earth. If you bounce the ball on Earth, there is more gravity. This creates more friction, which makes the balls stop sooner.