One of the major advantages of using a ball head is the simple operation it provides. A single knob is faster and easier to operate than multiple handles and levers. While one hand takes care of the knob, the other can be on the camera and positioning it as you look through the viewfinder. When you find that spot you’re looking for, give it a twist and away you go.
In addition to the simple activation of controls, the motion provided is equally elegant and simple — you might even say intuitive. A full range of rotation means there are no limits to which direction you can point the camera, and the motion feels quite natural and uninhibited. Your own hips and shoulders work on the same basis as the ball head: the ball and socket joint.
But besides the ergonomics and ease of use of the ball head, they’re also generally more compact than a pan head. There are no adjustment arms that hang off the head, and the single socket can be designed to occupy much less space than three separate hinge joints.
Plus they look cool.
Now of course there are downsides to every good thing out there. In the case of the ball head, it’s mainly the price. For a ball head of equal quality and capability to a pan head, the ball head will almost always cost more money. The main reason they cost more is because that precision ball and socket joint is much more difficult and expensive to manufacture than three decent clutched hinges.
The other downside of the ball head is with the strength and precision. Ball heads that are comparable in price to pan heads will typically support less weight (important for folks with big heavy lenses). The motion and the ability to stop the motion will also be of lower quality and capability than the pan head. It’s not to say that you can’t get a ball head to carry a heavy load with smooth operation — it’s just going to cost more.