Fixed blade broadheads are traditionally the broadhead of choice. A fixed blade broadhead is defined as a broadhead whose blades are permanently fixed in the open position. They generally cut on impact which is a much more efficient way of starting the wound channel, the blades cut into the hide and prevent the wound from closing fully, leading to an improved blood trail. Fixed blade broadheads also tend to be stronger than comparable mechanical broadheads. Because the blades are fixed within the head itself and do not move they are very rugged and reliable.
Fixed blade broadheads also offer higher penetration than mechanical broadheads, due in a large part to the fact that they cut on impact and do not loose energy to the process of opening. The only negatives with fixed blade broadheads is the fact that they tend to plane when shot out of high speed bows and can be knocked about by the wind. They also can be difficult to tune and tend to shoot to different points than field points. These negatives can be minimized by aligning the blades with the fletching.
Mechanical broadheads are relative new, and are making great inroads into the traditional fixed blades popularity. Mechanical broadheads tend to fly straight and shoot close to field points, this is due to the fact that the blades of a mechanical broadhead are hidden in flight and therefore are not affected by wind resistance to the same degree as fixed blades. Mechanical broadheads also offer larger cutting diameters which aid in faster more humane kills and easier tracking through better blood trails.
Mechanical broadheads do have some negatives, they tend to require a faster arrow speed to ensure penetration, this is due to the fact that they loose energy when they open. They can also malfunction and are more prone to deflection off bone, especially when they are opening. I have had many shots on deer with the rage 2" that hit ribs or shoulderblade and do not get a passthrough because of how wide the blades are. With a fixed tip the broadheads will punch through the shoulderblade.
As you can see the decision as to which broadhead to shoot is not as simple as picking whatever head looks cool or has the more attractive packaging. If you shoot a slower bow, under 250 fps or take longer shots, stick to fixed blade. If you have a very fast bow and limit your range, mechanicals offer many advantages.
No matter what head style you choose, nothing makes up for a poor shot, practice and hunt within your limitations.