It’s impossible to state one aspect of the golf ball is more important than the other, but this experiment shows the impact of removing a ball's dimples.
The small depressions found all over the ball ultimately determine velocity, launch and spin rate after it leaves the club face. Alter the depth of a dimple by as little as 1,000th of an inch and you could negatively affect the ball’s aerodynamics (lift and drag) while it’s rocketing through the air. In this case, the line between success and failure is razor-thin.
Ranking the pieces of a ball by importance is pointless because each plays a vital role. That said, even the most expensive ball in the world isn’t going anywhere without dimples.
If you need visual proof, take a look at this video Titleist recently published where four professionals were given the opportunity to test a dimpleless Pro V1.