Which one should be used and why from a users perspective.
Quick-Clot (US Based) made by Z-Medica uses Kaolinite which is a kind of clay and cannot be broken down by the body. When I have seen it used, it has burned on contact and needed to be cleaned out of the wound later. DoD users have reported difficulty in gaining formulaic documentation from the manufacturer.
Celox (UK Based) made by Celox Medical uses Chitosan, a natural polysaccharide, and is broken down by Lysozyme (found in human tears, saliva and mucus) into glucosamine (a natural sugar). It does not set off a clotting cascade, but clots the red blood cells it comes in contact with. From what I have seen it does not burn on contact and does not need to be cleaned out of the wound. I have no DoD information, but it is mandatory medical kit for the U.K. Military.
Personally - I'll take Celox over Quick-Clot.