[gryphonslair99]

Pan/Tilt head:
Pros: Easy to adjust in small increments just where you want it, one plane at a time. Sturdy.
Cons: Cumbersome to adjust. You are making adjustments one plane at a time. Head is cumbersome to haul around.
Personal Recommendation: Studio work, product shoots, architectural shoot, fine detail shoots.

Ball Head:
Pros: Easy to adjust quickly in all planes at once. Smaller in size. Stable, low center of gravity. Compact, easy to haul around.
Cons: Unless you are willing to pay big money for a top of the line ball head you will usually get a small amount of creep when you lock the ball. Unless you either pay attention or have one with separate friction control it is easy to loosen the ball lock too much and have camera flop unless you are supporting it with the other hand. Ball heads without a separate panning control are hard to use for panorama shots.
Personal Recommendation: Best all around compromise for a field setup. Easier to use and carry for general field work.

Side handle ball head:
Pros: Easy to adjust quickly and accurately. Stable with general use glass. With add on shutter release it is easy to adjust and shoot without moving your hand away.
Cons: Not as easy to haul around as a standard ball head. Not designed for bigger glass. Usually no separate panning feature.
Personal Recommendation: Excellent in studio for portrait type work.