Yes, you're partially right...if we drop both balls on Moon, they'll fall at the same time. Because there's (almost) no air on the Moon. The ball with less mass has less force of gravity to fight with air resistance on the Earth. Therefore, it falls slower.
Maybe this video can help to visualize: https://www.youtube.com/watch?v=Esa0kKECZvM
Even that is not correct. Air resistance is proportional to cross-section, and gravity is proportional to mass. A ball with less mass but much less cross section will fall faster. It has less "force of gravity", but it has much less air resistance. In other words, a marble will fall faster than a basketball when accounting for air resistance.
Note that the animation is inaccurate in any case because (assuming constant air density) the velocity of a falling ball will never decrease (until it hits the surface) if it started stationary.