Faster, lighter, more expensive (gives better image for those snobbish ones), looks more professional (since many pros are using it, again for the snobs),
Negs: can not control movement in one direction, although it is possible, expensive (again not for those who are snobbish), some are heavy though, difficult to adjust movements slightly (there is no long handle to adjust position as on a 3-way head)......
Maybe there are more points, these are what comes into my mind at this hour..
1 Less bulky with less things sticking out.
3 Faster to use
The main disadvanage is difficulty to move only in one plane, making precise adjustment a little more difficult.
I have 4 ball heads (two Arca Swiss B1, one Markins for travel with my "landscape gear", and one Leitz ball head for my really light travel) and one huge gitzo pan head. The pan head is used for my heaviest gear, when adjusting is really difficult using a ball head.
Ballheads have major engineering advantages over pan heads as follows:
Larger bearing surface, this spreads the load over a larger surface area, reducing both friction and also increasing stability. This feature is directly related to the size of the 'ball' in the ballhead.
Higher levels of rigidity. A well designed ballhead is a more rigid device than a pan head. Thus you should have lower levels of flexure at the camera with a well designed ballhead.
Reduced creep. Creep is movement that occurs when locking down a ballhead or pan head. Well designed ballheads (Arca, Graf, Large Fobas, Acratech Markin, Velbon, Kirk etc) should have zero or near zero levels of creep when the ball is locked.
The downside to ballheads are things such as flop (where the ball flops over) with longer lenses and heavier cameras, for example "view cameras" and they can be very expensive and are often quite touchy in operation.
Ultimately however for general use a Ballhead is superior for most applications, however there are times when pan heads are better. For example, a pan head is far superior with very large heavy technical cameras (view cameras) as the handles allow for more accurate control of unwieldy loads. A geared pan head is the ultimate for macro and large technical cameras. Cost wise the best geared pan heads are 3-4 times more expensive than ballheads of equivalent load rating.
For what it's worth, I use both and the choice of head depends on the camera and lens combination I'm using.